area of cuboid presentation

Volume Cube & Cuboid

Jan 07, 2020

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Volume. Volume Cube & Cuboid. Volume of a Prism. Volume of a Cylinder. www.mathsrevision.com. Capacity. Starter Questions. 10cm. Q1. Find the area of the triangle. 3cm. 4cm. Q2. Expand out and simplify 2w 2 – 3(2w – 5). www.mathsrevision.com. Q3. True or false.

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• 10 200 cm 3

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Volume Volume Cube & Cuboid Volume of a Prism Volume of a Cylinder www.mathsrevision.com Capacity

Starter Questions 10cm Q1. Find the area of the triangle. 3cm 4cm Q2. Expand out and simplify 2w2 – 3(2w – 5) www.mathsrevision.com Q3. True or false Q4. Rearrange into the form y = 2y – 3x + 7 = 0 Created by Mr.Lafferty

Volume Learning Intention Success Criteria • Know formulae. • We are revising volume of a cuboid. • Use formulae correctly. www.mathsrevision.com • Show working and • appropriate units. Compiled by Mr. Lafferty Maths Dept.

4cm 18 cubes fit the base. 3cm 6cm Volume of a cuboid www.mathsrevision.com = 1 centimetre cube = 1 cm³ 4 layers of 18 cubes = 4 x 18 = 72 centimetre cubes = 72 cm³ Compiled by Mr. Lafferty Maths Dept.

4cm 3cm 6cm A short cut ! height Area of rectangle breadth www.mathsrevision.com length Volume = 6 x 3 x 4 = 72 cm³ Volume = length xbreadth x height Compiled by Mr. Lafferty Maths Dept.

Heilander’s Porridge Oats Example Working Volume = l x b x h V = 18 x 5 x 27 V = 2430 cm³ 27cm 5 cm 18 cm Compiled by Mr. Lafferty Maths Dept.

Example Working Volume = l x b x h V = 2 x 2 x 2 V = 8 cm³ 2cm www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

Find the volume of the composite shape. VT = V1 + V2 7 cm VT = 105 + 720 5 cm VT = 825 cm3 3 cm 9 cm V1 = l x b x h www.mathsrevision.com = 3 x 5 x 7 V2 = l x b x h = 105 cm³ 10 cm = 8 x 10 x 9 8 cm = 720 cm³ Compiled by Mr. Lafferty Maths Dept.

Find the length the cuboid This just an equation. We know how to solve them ! 4 cm Volume = L x B x H V=200cm3 200 = L x 5 x 4 5 cm www.mathsrevision.com 200 = 20L 10 cm L 20L = 200 L = 10 Compiled by Mr. Lafferty Maths Dept.

Example Working Liquid Volume Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm³ 50 cm = 150 000 ml = 150 litres 30 cm 100 cm 1cm3 = 1 ml 1000 ml = 1 litre How much water can this fish tank hold in litres? So the fish tank can hold 150 litres of water. Compiled by Mr. Lafferty Maths Dept.

Volume Now try N5 Lifeskills Ex 1 Ch8 (page 74) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions Q1. True or false 2(x – 6) - 2(x + 6) = 0 Q2. Does 2.5 + 1.25 x 20 = 27.55 Explain your answer www.mathsrevision.com Q3. Factorise 2y2 + 3y +2 Q4. Calculate Created by Mr.Lafferty

Volume of Prisms Learning Intention Success Criteria • We are learning how to calculating volume of any • prism given area. 1. Calculate the volume for various prisms. 2. Solution must include appropriate units and working. www.mathsrevision.com

Volume of Prisms Definition : A prism is a solid shape with uniform cross-section www.mathsrevision.com Hexagonal Prism Cylinder (circular Prism) Triangular Prism Pentagonal Prism Volume = Area of Cross section x length

Volume of Solids Definition : A prism is a solid shape with uniform cross-section Q. Find the volume the triangular prism. www.mathsrevision.com Triangular Prism Volume = Area x length = 20 x 10 = 200 cm3 10cm 20cm2

Volume of Prisms Now try N5 Lifeskills Ex 2 Ch8 (page 75) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions Q1. Find the area of the parallelogram 7 Q2. Factorise 4x + 40 7 www.mathsrevision.com Q3. A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4. The speed of light is 300000000 metres per sec. True or false in scientific notation 3 x 108. Created by Mr.Lafferty

Volume of a Cylinder Learning Intention Success Criteria • To know formula. • We are learning how to derive the formula for the volume of a cylinder and apply it to solve problems. • Apply formula correctly. www.mathsrevision.com • Work backwards using formula.

Volume of a Cylinder The volume of a cylinder can be thought as being a pile of circles laid on top of each other. Volume = Area x height h = πr2 x h www.mathsrevision.com Cylinder (circular Prism) = πr2h

Volume of a Cylinder Example : Find the volume of the cylinder below. 5cm V = πr2h 10cm www.mathsrevision.com = π(5)2x10 Cylinder (circular Prism) = 250π cm3 = 784.5 cm3

Volume of a Cylinder Now try N5 Lifeskills Ex 3 Ch8 (page 77) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions 7cm www.mathsrevision.com Exchange Rate £1 =$1.50 Compiled by Mr. Lafferty Maths Dept.

Liquid Volume Learning Intention Success Criteria • Unerstand the term liquid volume. • We are learning the • term liquid volume using millilitres and litres. • Calculate volumes using 1ml and litres. www.mathsrevision.com • Answer to contain • appropriate units. Compiled by Mr. Lafferty Maths Dept.

Liquid Volume I’m a very small duck! How much water does this hold? 1 cm 1 cm 1 cm Volume = x b x h l = 1 cm³ A cube with volume 1cm³ holds exact 1 millilitre of liquid. A volume of 1000 ml = 1 litre. Compiled by Mr. Lafferty Maths Dept.

Orange Flavour Example 1 Liquid Volume Working Volume = l x b x h V = 6 x 3 x 12 12 cm V = 216 cm³ = 216 ml 3 cm www.mathsrevision.com 6 cm So the carton can hold 216 ml of orange juice. Remember: 1 cm³ = 1 ml How much juice can this carton hold? Compiled by Mr. Lafferty Maths Dept.

Example 2 Working Liquid Volume Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm³ 50 cm = 150 000 ml = 150 litres 30 cm 100 cm 1cm3 = 1 ml 1000 ml = 1 litre How much water can this fish tank hold in litres? So the fish tank can hold 150 litres of water. Compiled by Mr. Lafferty Maths Dept.

Liquid Volume Now try N5 Lifeskills Ex 4 Ch8 (page 80) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

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Let’s play a game! . }. =?. =?. =?. Guess cube roots. Recall: What is a Cube Root?. The edges of a cube all have the same measure: let’s call it s . s. The volume V of this cube is then given by the formula. s. s. We can also write. V = s 3. s = 3 V. We say that

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Surface Area of a Prism Cubes and Cuboids.

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Presentation on theme: "Surface Area of a Prism Cubes and Cuboids."— Presentation transcript:

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• Surface Area of a cuboid – Explanation & Examples

Surface Area of a Cuboid – Explanation & Examples

In geometry, a cuboid is a 3-dimensional figure with a length, width, and height. A cuboid has 6 rectangular faces. Ultimately, a cuboid has the shape of a rectangular prism or a box.

In a cuboid, the horizontal longer side is the length (l), and the shorter horizontal side is the width (w) or breadth (b). The height (h) of a cuboid is the vertical side.

The surface area of a cuboid is the sum of the area of the 6 rectangular faces that cover it.

In this article, we will learn how to find the surface area using a cuboid formula’s surface area.

How to Find the Surface Area of a Cuboid?

To find the surface area of a cuboid, you need to calculate the area of each rectangular face and then sum up all the areas to get the total surface area i.e.

• Area of the top and bottom face = lw+ lw = 2lw
• Area of the front and back face = lh+ lh = 2lh
• Area of the two side faces = wh+ wh = 2wh

The total surface area of a cuboid is equal to the sum of the face areas;

Surface area of cuboid = 2lw + 2lh + 2wh 

Note: The cuboid’s total surface area is not the same as the lateral surface area of a cuboid. The lateral surface of a cuboid is the sum of the area of the rectangular faces excluding the top and bottom face;

Lateral surface area of a cuboid ( LSA ) = 2h (l +b)

Surface area of a cuboid formula

From the above illustration, the formula for the total surface area of a cuboid can be represented as:

Total surface area of a cuboid (TSA) = 2 (lw + wh + lh)

The units for the surface area of a cuboid are square units.

Let’s practice some example problems below.

The dimensions of a cuboid are given as follows:

Length = 5 cm

Width = 3 cm

Height = 4 cm.

Find the total surface area of the cuboid.

By the formula,

Total surface area of a cuboid = 2 (lw + wh + lh)

Substitute.

TSA = 2(5 x 3 + 3 x 4 + 5 x 4)

= 2(15 + 12 + 20)

= 2 x 47 = 94 cm 2

Therefore, the total surface area of the cuboid is 94 cm 2

The surface area of a cuboid is 126 ft 2 . If the cuboid’s length and height are 6 feet and 3 feet, find the width of the cuboid.

Total surface area = 126 ft 2

Length = 6 ft

Height = 3 ft

⇒126 = 2 (lw + wh + lh)

⇒126 = 2 (6w + 3w + 6 x 3)

⇒126 = 2(9w + 18)

⇒126 = 18 w + 36

Subtract by 36 on both sides and then divide by 18

Therefore, the width of the cuboid is 5 feet.

Given the dimensions of a cuboid as:

Length = 10 m

width = 5 width

Height = 9 m

By how much is the total surface area of the cuboid more than the lateral surface area?

Total surface area = 2 (lw + wh + lh)

= 2 (10 x 5 + 5 x 9 + 10 x 9)

= 2(50 + 45 + 90)

TSA = 2 x 185

The lateral surface area of a cuboid = 2h (l + b)

= 2 x 9(10 + 5)

Total surface area – lateral surface area = 370 – 270

Therefore, the total surface area of the cuboid is 100 m 2 more than the lateral surface area.

The length and width of a cardboard are 20 m by 10 m, respectively. How many cuboids can be made from the cardboard if each cuboid must be 4 m long, 3 m wide, and 1 m high.

Area of the cardboard = l x w

Total surface area of the cuboid = 2 (lw + wh + lh)

= 2 (4 x 3 + 3 x 1 + 4 x 1)

= 2 (12 + 3 + 4)

The number of cuboids = area of the cardboard/total surface area of a cuboid

= 200 m/38 m 2

= 5 cuboids

Compare the total surface area of a cube of length 8 cm and a cuboid of length 8 cm, width, 3 cm, and height, 4 cm.

Total surface area of a cube = 6a 2

= 2(8 x 3 + 3 x 4 + 8 x 4)

= 2(24 +12 + 32)

Therefore, the surface area of the cube is more than the surface area of the cuboid.

Practice Questions

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• Math Article

In geometry, a cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid. A cuboid is also called a  rectangular prism .  A cuboid with six square faces is called a cube . An example of a cuboid in real life is a rectangular box. 

In Maths, we can observe other shapes which are exactly the same as cuboid, they are rectangular cuboid, rectangular box, right rectangular prism, right cuboid, rectangular parallelepiped, and rectangular hexahedron. Let us learn here details of cuboids with examples.

What is a Cuboid?

A cuboid is a three dimensional solid that has 6 faces (rectangular), 8 vertices and 12 edges. A cuboid has three dimensions such as length, width and height. A perfect cuboid is said to be a cuboid that has integer edges.

If we consider Euler’s formula, then the relation between Faces (F), Vertices (V) and Edges (E) of a cuboid satisfies the equation:

F + V = E + 2

6 + 8 = 12 + 2

Cuboid Shape

Faces, Edges and Vertices of Cuboid

A cuboid has 6 faces, 8 vertices and 12 edges. All these can be shown using notation as given below:

Faces of Cuboid

A Cuboid is made up of six rectangular faces. In the above-given figure, the six faces are:

The pair of opposite and parallel faces of the given cuboid are:

ABCD and EFGH (top and bottom faces respectively)

ABFE, DCGH, and DAEH, CBFG (opposite and parallel faces which are adjacent to the top and bottom faces of the cuboid)

For each face, we can write the remaining faces as their adjacent faces such as the face ABCD is the adjacent face to ABFE, BCGF, CDHG, and ADHE.

Edges of Cuboid

The sides of all the rectangular faces are referred to as the edges of the cuboid. As we know, there are 12 edges for a cuboid. They are AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF and CD respectively. Also, the opposite sides of a rectangle are equal. Therefore,

• AB = CD = GH = EF
• AE = DH = BF = CG
• EH = FG = AD = BC

Vertices of Cuboid

The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid and a cuboid has 8 vertices.

From the given cuboid figure, the 8 vertices are A, B, C, D, E, F, G and H.

Let us have a look at the visualization of faces, edges and vertices of a cuboid.

Properties of Cuboid

• A cuboid has 6 faces, 12 edges and 8 vertices
• The faces of the cuboid are all rectangular in shape
• Opposite edges of the cuboid are parallel to each other
• Cuboid has three dimensions: length, width and height
• Angles formed at the vertices of the cuboid are all 90 degrees

Surface Area of Cuboid

The surface area of any three-dimensional shape is the total region covered by all its faces. In the same way, the surface area of a cuboid is the sum of the areas of all its six rectangular faces. The surface area of the cuboidal box can be divided into two types namely lateral surface area and total surface area. The formulas for these can be derived from the figure given below.

Let l, b and h be the length, breadth and height of a cuboid respectively.

From the figure given above,

• AB = CD = EF = GH = l
• BC = AD = EH = FG = b
• CG = BF = AE = DH = h

Cuboid Lateral Surface Area

Lateral surface area (LSA) of a cuboid is the sum of areas of all faces except the top and bottom faces.

Lateral surface area of the cuboid = Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH

= (AD × DH) + (BC × CG) + (AB × BF) + (CD × BC)

= (b × h) + (b × h) + (l × h) + (l × h)

= 2(b × h) + 2(l × h)

= 2h(l + b)

Cuboid Total Surface Area

Total surface area (TSA) of a cuboid is the sum of the areas of all its rectangular faces.

Area of face EFGH = Area of Face ABCD = (l × b)

Area of face BFGC = Area of face AEHD = (b × h)

Area of face DHGC = Area of face ABFE = (l × h)

Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces

= Area of (ABCD + EFGH + BFGC + AEHD + DHGC + ABFE)

= (l × b) + (l × b) + (b × h) + (b × h) + (l × h) + (l × h)

= 2lb + 2bh + 2hl

= 2(lb + bh + hl)

Volume of Cuboid

The volume of a solid is equal to the product of the base area and its height. Thus, the volume of cuboid is equal to the product of the base rectangular face and height.

Volume = (Length × Breadth) × Height

= (l × b) × h

Diagonal of Cuboid

The length of the diagonal of a cuboid of dimensions l, b and h is given by the formula:

This formula is for the length of space diagonals of a cuboid. Whereas the face diagonals of the cuboid are the diagonals drawn by joining the vertices on a face of the cuboid. For each face there are two diagonals, so the total face diagonals that can be drawn in a cuboid are 12 (6 faces x 2).

Perimeter of Cuboid

The perimeter of a cuboid will be the sum of the lengths of all the edges. Thus, from the above figure 2,

• AB = CD = EF = GH = l (length)
• BC = AD = EH = FG = b (breadth)
• CG = BF = AE = DH = h (height)

Perimeter of the cuboid = AB + CD + EF + GH + BC + AD + EH + FG + CG + BF + AE + DH

= (l + l + l + l) + (b + b + b + b) + (h + h + h + h)

= 4l + 4b + 4h

= 4(l + b + h)

Cuboid Formulas

The table below shows the formulas of a cuboid of length (l), breadth (b) and height (h).

The net of a solid shape is the plane obtained by unfolding it across a line. This net will again form the original solid when we fold it. The number of different nets for a cuboid or rectangular cuboid with 3 different lengths is 54.

Click here to learn more about nets of 3d shapes .

Similarly, the nets of a cuboid can be shown in different ways.

Related Articles

• Cube and cuboid
• Volume of a cube
• Surface areas and volumes
• Difference between Cube and Cuboid

Solved Examples on Cuboid

Below are some example problems solved using the formulas of cuboids.

Find the volume of a cuboid of length 10 cm, breadth 8 cm and height 4 cm.

Length = l = 10 cm

Breadth = b = 8 cm

Height = h = 4 cm

Volume = lbh

= 10 × 8 × 4

Calculate the lateral and total surface area of a cuboid of dimensions 12 cm × 7 cm × 5 cm.

Given dimensions of a cuboid are: 12 cm × 7 cm × 5 cm

i.e., l = 12 cm, b = 7 cm, h = 5 cm

Lateral surface area (LSA) = 2h(l + b)

= 2 × 5 (12 + 7)

Total surface area (TSA) = 2(lb + bh + hl)

= 2(12 × 7 + 7 × 5 + 5 × 12)

= 2(84 + 35 + 60)

Practice Problems

Find the total surface area and volume of cuboid whose dimensions are:

• Length = 3 cm, Width = 2 cm and Height = 1.5 cm
• Length = 6 cm, Width = 4 cm and Height = 3 cm
• Length = 7.5 cm, Width = 3.5 cm and Height = 5 cm

Frequently Asked Questions on Cuboid

What is the definition of a cuboid, how many edges and corners does a cuboid has, what is the difference between cube and cuboid.

The main difference between the cube and cuboid is their faces, i.e. the cube has six square-shaped faces, whereas the cuboid has six rectangular faces. That means, all the edges of the cube are equal and the edges of a cuboid can be written as 3 groups of equal edges.

What is the cuboid formula?

The formulas of cuboid are:

Total surface area = TSA = 2(lb + bh + hl)

Volume (V) = lbh

Perimeter (P) = 4(l + b + h)

Diagonal (D) = √(l^2 + b^2 + h^2)

What is the difference between the cuboid and a rectangular prism?

There is no difference between the cuboid and rectangular prism since both will have 6 rectangular faces, 8 vertices and 12 edges. Also, both look the same as a box.

Can a cuboid have a square face?

As we know, a cube is a special kind of cuboid with all its edges equal in length. Hence, a cuboid can have a square face.

How do you find the area of a cuboid?

To find the total surface area of a cuboid, add the areas of all six faces. Suppose l, b and h be the length, breadth and height of a cuboid, then the total surface area will be 2(lb + bh + hl).

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Surface Area Cuboid and Cylinder 18Nov09 - PowerPoint PPT Presentation

Surface Area Cuboid and Cylinder 18Nov09

The formula for the perimeter of a rectangle is: l h l h. l x h x l x h. l x w 2 ... 4. the name for the perimeter of a circle is: radius. diameter ... – powerpoint ppt presentation.

• The formula for the perimeter of a rectangle is
• L x H x L x H
• 2. The formula for the area of a rectangle is
• 3. The Greek letter pi ? is approximately
• 4. The name for the perimeter of a circle is
• Circumference
• 5. The radius of a circle is
• The distance from the centre to the edge
• The distance across a passing through the centre
• The distance all the way
• 6. The diameter of a circle is
• Half of the radius
• Half the circumference
• Twice as big as the radius
• 7. The formula for the circumference of a circle is
• 9. ?r2 means
• 11. The little number 2 on area measures (4 cm2) means that
• The answers is times 2
• The units are square cm.
• The units are doubled

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Surface Area of a Cuboid Video

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Surface area of cuboids

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Key learning points.

• In this lesson, we will learn how to calculate the surface area of cuboids.

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

Starter quiz

5 questions.

6 Questions

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Unit maths / volume and surface area of prisms.

17 Cuboid Examples in Real Life

A cube is a three-dimensional geometric shape that consists of 6 rectangle-shaped faces, 12 edges, and 8 vertices. It is formed by extending a two-dimensional rectangle in one direction. The 6 rectangles used to form a cuboid geometric shape are aligned at right angles to each other. The surface area of a cuboid is given as twice the sum of the product of length and breadth, breadth and height, and height and length. The volume of a cuboid can be calculated by evaluating the product of its length, breadth, and height. The cuboid geometric shape falls under the category of a convex polyhedron.

Examples of a Cuboid

The most popular example of cuboid-shaped objects used in real life is a brick. Each face of a brick is rectangular in shape, and there are a total number of six such faces.

2. Packaging Boxes

Corrugated boxes are manufactured in a number of sizes and shapes. One of the most common shapes of a corrugated box is a cuboid.

3. Mattresses

You can easily observe the cuboid geometric shape in real life by looking at the shape of mattresses.

Books are a perfect example of cuboid-shaped objects present around us.

A shoebox forms an explicit example of cuboid-shaped objects used in real life because it consists of six rectangular faces attached to each other at an angle of 90 degrees.

6. Cabinets

The drawers and cabinets used to store objects are mostly constructed in the shape of a cuboid that is hollow from the top or front. Hence, the cabinets form a classic example of the cuboid-shaped objects present around us.

7. Lunch Box

Lunch boxes are available in a variety of shapes and sizes out of which the most popular shape of a lunch box is a cuboid.

8. Match Box

A matchbox is a small box made up of cardboard that has a sliding drawer. The shape of this cardboard drawer is a cuboid as well as the shape of the matchbox is a cuboid.

9. Tissue Box

Tissue boxes or napkin holders are cuboid-shaped containers made up of cardboard used to hold tissue papers. They consist of a small opening from where the napkins can be dispensed easily.

10. Microwave

A microwave oven consists of 6 rectangular faces inclined at an angle of 90 degrees to each other. Hence, it is yet another example of the cuboid-shaped objects used in everyday life.

11. Fish Tank

A fish tank is a glass container in which the pet aquatic animals and plants are kept. These containers are usually shaped like a cuboid geometric figure that is hollow from one side. Hence, fish tanks form a great example of cuboid-shaped objects that we can easily see in our houses.

12. Juice Box

A juice box is a cardboard carton that is generally cuboidal in shape. Hence, it is yet another example of cuboid-shaped objects used in daily life.

13. Refrigerator

Refrigerators are yet another example of cuboid-shaped objects used in real life.

Most of the radios, stereo players, and other similar devices are cuboid in shape. Hence, they form a perfect example of cuboid-shaped objects present in real life.

15. Deck of Cards

Playing cards are rectangular in shape. If all the playing cards are placed one on top of another, it forms a deck of cards that resembles the shape of a cuboid geometric shape.

16. Electronic Gadgets

Most of the communication electronic gadgets such as a cell phone, laptop, pen drive, tablet, etc., are cuboidal in shape. Hence, the gadget that you are using to browse this article is a prominent example of a cuboid geometric shape.

17. Drugs and Medicine

Pills or medicines are available in a number of shapes such as a sphere, a cube, or a cuboid. The cuboidal pills are a perfect example of cuboid-shaped objects used in daily life.

Related Posts

10 Semicircle Examples in Real Life

15 Arc Examples in Real Life

5 Octahedron Examples in Real Life

20 Cylinder Examples in Real Life

18 Oval Examples in Real Life

17 Parallel Lines Examples in Real Life

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Volume of Cuboid: A Comprehensive Guide

Curious about finding the volume of a cuboid? It's calculated by multiplying length, width, and height: V = l × w × h. This blog offers a detailed explanation, including real-life examples and practical tips to calculate the Volume of a Cuboid. Discover how understanding cuboid volume can be applied in various scenarios!

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Stuck figuring out how much packing to bring for that big move?  Ever wondered exactly how much water fits in that rectangular fish tank?  The answer lies in a secret weapon of the 3D world: the volume of a cuboid.  This essential concept unlocks the mysteries of any box-shaped object.  Don't be fooled by its seemingly simple form!   

This blog is your go-to guide to conquering the volume of a cuboid.  We'll break down the formula, tackle real-life examples, and equip you with the skills to measure the volume of any cuboid with confidence.  So, ditch the guesswork and become a master of cuboid volume – your boxes (and fish!) will thank you! 

Table of Contents 

1) Formula for Calculating the Volume of a Cuboid 

2) Practical Examples of Cuboid Volume Calculation 

a) Calculating the Volume of a Cube 

b) Determining the Volume of a Cuboid 

c) Volume of a Cuboid with Different Units 

d) Finding the Width of a Cuboid Given Its Volume  

e) Finding the Length of a Cuboid Given Its Volume  

3) Conclusion 

Formula for Calculating the Volume of a Cuboid 

A cuboid is a three-dimensional shape (3D) with six rectangular faces, and its volume can be found by multiplying its length (l), width (w), and height (h). The formula for the Volume (V) of a Cuboid is: 

where: 

a) l is the length of the cuboid 

b) w is the width 

c) h is the height 

This formula applies to all cuboids, regardless of the specific dimensions of each side. By multiplying these three dimensions, you get the total space occupied by the cuboid.  

Practical Examples of Cuboid Volume Calculation 

To better understand how to apply the volume formula, let's go through some practical examples involving different scenarios. 

1) Calculating the Volume of a Cube 

A cube is a special type of cuboid where every side is of equal length. Therefore, if a cube has a side length of a, the volume formula simplifies to:

Example: I f a cube has a side length of 4 units: 

Cube the side length: 43=64 

Result: The volume of the cube is 64 cubic units. 

2) Determining the Volume of a Cuboid 

For a standard cuboid with different length, width, and height measurements, use the general formula. 

Example: If a cuboid has a length of 5 units, a width of 3 units, and a height of 2 units: 

Multiply the length, width, and height: 

The volume of the cuboid is 30 cubic units. 

3) Volume of a Cuboid with Different Units 

When dealing with different units, it's crucial to convert them to the same unit before computing the volume. 

Example: If a cuboid has a length of 1 meter, a width of 50 centimeters, and a height of 200 millimeters, convert all measurements to the same unit (e.g., meters): 

Convert the width and height to meters:  

Multiply the converted dimensions: 

The volume of the cuboid is 0.1 cubic meters. 

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4) Finding the Width of a Cuboid Given Its Volume  

Sometimes, you may know the volume and two of the dimensions and need to find the third dimension. If the volume (V), length (l), and height (h) are known, you can rearrange the formula to find the width (w): 

If a cuboid has a volume of 60 cubic units, a length of 5 units, and a height of 3 units: 

Substitute the known values into the rearranged formula: 

The width of the cuboid is 4 units. 

5) Finding the Length of a Cuboid Given Its Volume 

Similarly, if the volume (V), width (w), and height (h) are known, you can find the length (l) by rearranging the formula: 

Example: If a cuboid has a volume of 120 cubic units, a width of 4 units, and a height of 5 units: 

 The length of the cuboid is 6 units. 

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Conclusion 

Congrats! You've unlocked the secrets of the cuboid! Now you can measure the volume of Cuboid shaped boxes, containers, and anything else with rectangular sides. Remember, practice makes perfect. So next time you see a box, try calculating its volume using the formula you learned. With a little more confidence, you can tackle even more complex 3D shapes! 

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Frequently Asked Questions

The rule for the volume of a cuboid is to multiply its length, width, and height. The formula is V = l×w×h .   

The properties of a cuboid's volume include being proportional to its dimensions and measured in cubic units. Doubling any dimension doubles the volume, reflecting its three-dimensional space occupancy. 

To get the surface area of a cuboid, sum the areas of all six faces using the formula: SA=2lw+2lh+2wh. 

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Darke to give soil, water presentation.

EVENT COMING — Working on details of Thursday’s presentation by Rick Darke are, from left, Aaron Dodds, project manager of the Jefferson Soil and Water Conservation District, and Ken Perkins and Andrew Morris, members of the district’s board of supervisors. Darke, a landscape ethicist, author and photographer, will speak at 7 p.m. Thursday in the auditorium of Indian Creek High School. There is no charge to attend. -- Ross Gallabrese

WINTERSVILLE — When Rick Darke takes the stage inside the auditorium at Indian Creek High School on Thursday evening, he will be talking about how parts of our area look now while offering a vision of what they can become.

A landscape ethicist, author and photographer, Darke’s 7 p.m. appearance will come at the end of a three-day visit to the area. He said he will spend Tuesday and Wednesday examining and documenting parts of the county and then incorporate those observations and photographs — including images from a drone — into his presentation, “Celebrating the Strength and Resilience of America’s Living Landscapes.”

“My tact lecturing for decades has been to get up-to-the-minute photos that integrate time, places and community,” he explained.

He’ll be looking at several different areas of land controlled by the Jefferson Soil and Water Conservation District, which is bringing Darke to the area and sponsoring Thursday’s presentation. There is no charge to attend.

“Soil and water has several properties that we are working to develop,” explained Aaron Dodds, project manager for the district. “We want to make sure they are cutting-edge properties that will attract people to the area. We were looking at people who had developed similar projects, and he was one of the designers we had a focus on.”

Darke has been helping to transform areas for more than a quarter of a century. He said he enjoys looking for ways to incorporate an area’s industrial past with modern landscapes. He’ll be offering a different perspective on the sustainable landscapes people see around them every day, according to a synopsis provided by the district, as well as using his experience to show how parts of the district’s property can be transformed into recreation and learning spaces.

There are a couple of examples in our region of the impact the Landenberg, Pa.-based Darke has made — those include the Carrie Blast Furnaces National Historic Landmark in the Pittsburgh suburb of Swissvale, and the land around Fallingwater, the iconic house architect Frank Lloyd Wright built for Edgar Kaufmann in the Laurel Highlands of Western Pennsylvania.

Carrie furnaces Nos. 6 and 7 once were part of the U.S. Steel Homestead Works. They are the only two non-operative blast furnaces left in the region, according to the Rivers of Steel National Heritage Area.

“When I’m talking about what’s possible, I’m talking from first-hand evaluations,” Darke said. “The goal of this project — like the furnace project — is making a lot with a little and being efficient with our resources, the time of the people who are working on it and the volunteers. We want to keep it authentic and grounded.”

In total, Dodds explained, soil and water has about 575 acres to work with in the Piney Fork and Quaker Ridge areas as well as its hellbender preserve, and is looking to open up public access to about half of it. The work will start in the area of the old mining town of Piney Fork and will include a five-mile trail and redevelopment of the railyard into a park setting.

Funding for those projects had been included in the conservation district’s Appalachian Community Grant application. The program, which distributed $500 million across the 32 counties in Ohio that lay in the Appalachian region, largely bypassed our area, with only Adena receiving $4.5 million for streetscape and building renovation work.

While missing out on that money was disappointing, Dodds said the district is pushing forward with its plans to develop those areas.

“Just because we were not successful in getting the grant funding doesn’t mean we have stopped working,” Dodds said. “Rick’s presentation will capture some of the things we are developing. It will show how we can contribute to our property, and will show things other municipalities can do and that homeowners can bring to their own backyards.”

Darke, who will be making his second trip to the area, said he enjoys working with the conservation district.

“Aaron and Wendee (Dodds, the district’s natural resource specialist and operations manager) and everyone at the district have a good aesthetic and design sense, and they really want to do something for the community. They are community projects — they are making life better for everyone in the area.”

Part of what he will be looking for are the ways what’s left of the railroad — the meeting points where lines cross each other, known as frogs, or common crossings, for example — can be incorporated into the work.

“Those common crossings can be a place where people from around the community can come together,” Darke added.

Developing those properties and opening up more area for outdoor recreation is important for the region to grow, Dodds said, and will offer new opportunities for people to explore parts of the area that hold a rich history.

“One of the things, especially in government, that you hear all of the time is that there’s nothing for people to do here in the county,” he said. “Quality of life is very critical to retaining and attracting people to the area. The natural beauty of our area is unparalleled — it is gorgeous.”

Completing projects in the district’s nearly 600 acres will make that beauty accessible — and encourage people to explore the outdoors.

“It’s really about getting some of these kids less screen time and more green time where they can experience nature and all of its glory,” Dodds added. “If you’re walking along a creek and see a kingfisher, and then a bald eagle flies over and a box turtle crosses in front of you, it’s a lifetime memory.”

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Volume of Cubes and Cuboids - Full lesson

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

23 August 2024

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The lesson covers: Finding the volume of a cuboid Finding the volume of a cube Finding the a missing side length of a cuboid given its volume and two sides. Finding the a missing side length of a cube given its volume.

Contains I do - We Do - You Do Cycles with AFL opportunities via MWB and RAG. This lesson is a comprehensive look into the topic. The Powerpoint is 100% animated and does not require the teacher to write, allowing them to circulate with a clicker/ tablet and monitor students.

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