lesson 5 problem solving practice volume of pyramids

Volume Of A Pyramid

In these lessons, we will learn

• what is a pyramid?
• how to find the volume of a pyramid with rectangular or square bases.
• how to find the volume of a pyramid with different types of bases.
• how to solve word problems about pyramids.
• how to demonstrate the relationship between the volume of a pyramid and the volume of a prism with the same base and height.

Related Pages Volume Formulas Volume Of Cylinders Explanations For The Surface Area Formulas More Geometry Lessons

Solid geometry is concerned with three-dimensional shapes.

A pyramid is a solid with a polygon base and connected by triangular faces to its vertex. The lateral faces meet at a common vertex . The height of the pyramid is the perpendicular distance from the base to the vertex.

A pyramid is a regular pyramid if its base is a regular polygon and the triangular faces are all congruent isosceles triangles. The pyramid is named after the shape of its base. A rectangular pyramid has a rectangle base. A triangular pyramid has a triangle base.

Volume Of Pyramids

The volume of a pyramid is equal to one-third the product of the area of the base and the height.

The volume of a pyramid is given by the formula:

Worksheet: calculate the volumes of square pyramids

Worksheet: calculate the volumes of prisms & pyramids

Example: Find the volume of a pyramid with a rectangular base measuring 6 cm by 4 cm and height 10 cm.

Example: The following figure is a right pyramid with an isosceles triangle base. Find the volume of the pyramid if the height is 20 cm.

Solution: First, we have to calculate the area of the base.

To do that, we would need to get the height of the isosceles triangle that forms the base.

Volume of a Pyramid with Rectangular or Square Base

This video gives the formula to find the volume of a pyramid and uses it to find the volume of a pyramid with a rectangular base.

How to find the volume of a pyramid?

Example: Find the volume of a pyramid given s = 9ft, h = 5ft, l = 8ft.

How to calculate the volume of a pyramid?

Example: The base of the following pyramid is a square. What is the volume of the pyramid?

Volume of a pyramid: Calculate height using Pythagorean Theorem

Volume Of Pyramid With Different Types Of Bases

Volume Of A Triangular And Square Pyramid

How to find the volume of a square pyramid and a triangular pyramid and compare how they are the same and how they are different?

Volume of a Hexagonal Pyramid

Example: Find the volume of a hexagonal pyramid that has a height of 8 and a base edge of 10.

Word Problems About The Volume Of Pyramids

Find the height of a pyramid given the volume and base dimensions.

Example: The base of the following pyramid is a square. If the volume of the pyramid is 360 ft 3 , what is the missing length?

Example: The volume of a pyramid is 80cm 3 , base is a triangle, find the height.

Volume of a Pentagonal Pyramid

Example: Find the surface area of a regular pentagonal pyramid given an altitude of 4 and a slant height of 5. Given the altitude and slant height we can find the apothem. Using the apothem, we can find the area of the base. The volume of the pyramid is 1/3 the area of the base multiply by the height.

• A square pyramid has a height of 7 m and a base that measures 2 m on each side. Find the volume of the pyramid. Explain whether doubling the height would double the volume of the pyramid.
• The volume of a prism is 27 in 3 . What is the volume of a pyramid with the same base and height?

Demonstrate the formula of the volume of a pyramid

This video will demonstrate that the volume of a pyramid is one-third that of a prism with the same base and height and that the volume of a cone is on-third that of a cylinder with the same base and height. This is not a formal proof.

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Volume of a Pyramid Practice Questions

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Volume of a Pyramid

Learn how to find the volume of a pyramid., volume of a pyramid lesson, pyramid volume formula.

The formula for volume of a pyramid is given as:

• V = 1 ⁄ 3 lwh

Where V is the volume, l is the base's length, w is the base's width, and h is the height of the prism.

Volume of a Pyramid Example Problems

Let's go through a couple of example problems together to practice finding the volume of a pyramid.

Example Problem 1

Find the volume of a pyramid with a base length of 6, base width of 6, and prism height of 3.

• Let's plug the given dimensions into the volume formula. This gives us:
• V = 1 ⁄ 3 (6)(6)(3) = 36
• The volume is 36.

Example Problem 2

Find the volume of a pyramid with a base length of 3, base width of 6, and a height of 10.

• V = 1 ⁄ 3 (3)(6)(10) = 60
• The volume is 60.

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Volume of a Pyramid Worksheets

Work out the volume of the pyramids with rectangular, triangular and polygonal base faces. Calculate the volume by plugging in the measures expressed as integers and decimals in the appropriate formulas. The 8th grade and high school printable worksheets are classified into two levels. Level 1 comprises polygons with 3 or 4-sided base faces, while level 2 includes polygonal base faces. Practice finding the missing measures as well. Explore some of these worksheets for free!

Finding Volume using Base Area | Integers

Jump-start your learning with this batch of PDF worksheets for 8th grade and 9th grade students on mixed pyramids featuring rectangular and triangular pyramids. Apply apt formulas to find the volume using the base area measure expressed as integers.

• Download the set

Finding Volume using Base Area | Decimals

Advance to the next level consisting of pyramids whose base faces are rectangles or triangles, and the base area is indicated as decimals. Multiply the base area with the height and divide by 3 to compute the volume.

Volume of Rectangular Pyramids

Exclusively dealing with rectangular pyramids, these PDF worksheets for 9th grade and 10th grade students are a must-have for thorough knowledge and practice in finding the volume of rectangular pyramids offering varied levels of difficulty.

(24 Worksheets)

Volume of Triangular Pyramids

Make strides in your practice with these printable worksheets on finding the volume of triangular pyramids or tetrahedrons. Try the easy, moderate and challenging levels with integer and decimal dimensions.

Finding Volume of Polygonal Pyramids using Apothem | Level 1

Another essential step is to determine the volume of pyramids with polygonal base faces. Plug in the apothem(a), number of sides(n), side length(s) and height(h) in the formula V = 1/6 * ansh and compute the volume.

Volume of Polygonal Pyramids using Side length or Perimeter | Level 2

The side length or perimeter and height are provided. First, find the apothem (apothem = side / 2 tan (180/n)), and then assign the known values in the volume formula to solve for volume of polygonal pyramids.

Volume of Pyramids | Level 1 - Integers - Easy

The easy level contains pyramids with integer dimensions ≤ 20. One-third of the base area of the square, rectangle or a triangle multiplied by the height results in the volume of the pyramid. Recommended for grade 8 and grade 9 children.

Volume of Pyramids | Level 1 - Integers - Moderate

Polish up your skills in finding the volume of pyramids with this section of high school geometry worksheets presenting pyramids as 3D shapes and in the word format with 3 or 4-sided base faces involving integer dimensions ≥ 20.

Volume of Pyramids | Level 1 - Decimals

Scale new heights as you practice solving for volume with these pdf worksheets posing a challenge with decimal dimensions. Apply relevant formula, substitute and calculate the volume of each pyramid.

Volume of Pyramids | Level 2

With the sides of the base face, increases the level of difficulty. Figure out the volume of the triangular, rectangular and polygonal pyramids applying suitable formulas and bolster skills.

Volume of Pyramids | Missing Measure

Motivate learners to give these printable worksheets a quick try. All they have to do is simply rearrange the formula, making the missing measure (x) the subject, plug in the known values and solve!

Related Worksheets

» Volume of Prisms

» Volume of Mixed Shapes

» Volume of Composite Shapes

» Volume of Cones

» Volume of Spheres

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Lesson Plan: Volumes of Pyramids Mathematics • Second Year of Secondary School

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This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the volume of a pyramid and solve problems including real-life situations.

Students will be able to

• recall the formula for the volume of a pyramid,
• a triangle,
• a quadrilateral,
• a regular polygon with more than 4 sides (pentagon, hexagon, etc.),
• an arbitrary polygon with a given area,
• calculate a missing length of a pyramid when given its volume,
• use knowledge of the volume of a pyramid to solve problems presented as real-life systems.

Prerequisites

Students should already be familiar with

• the slant height and the perpendicular height of a pyramid,
• right pyramids,
• the Pythagorean theorem,
• trigonometry,
• finding the area of an n-sided regular polygon.

Students will not cover

• the surface area of a pyramid.

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Volume of Pyramids

Subject: Mathematics

Age range: 14-16

Resource type: Lesson (complete)

Last updated

26 November 2020

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One FULL LESSON on finding the volume of pyramids.

Contents of download:

• Clicker version : Normal PowerPoint lesson with which you can use a clicker / mouse / keyboard to continue animations and show solutions.
• Triggered version : Normal PowerPoint lesson with which you can use the solutions button to continue animations and show solutions (best on an interactive whiteboard).
• Worksheets (including example and extension).

We are learning about: The volume of a Pyramid We are learning to: Calculate the volume of a pyramid.

Differentiated objectives:

• Developing learners will be able to calculate the volume of a pyramid.
• Secure learners will be able to find a missing length in a pyramid given its volume.
• Excelling learners will be able to solve unfamiliar problems using their knowledge of calculating the volume of a pyramid.

Main: Walkthrough examples followed by practice questions on worksheets. Starts with basic calculating the volume moving on to finding missing lengths of a pyramid. All solutions given on PPT and in worksheet format.

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