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VOLUME: COMPOSITE FIGURES

Unit Overview

In this unit, students will identify the volume of composite figures.

Key Vocabulary

Composite Figures

A composite figure is a three-dimensional figure that is the combination of two or more similar figures. Solid figures such as prisms, cylinders, pyramids, cones, and spheres are used to make 3-dimensional solids called a composite of multiple shape or composite figures.

Let's Practice - Composite Figures

1. For each of the composite figures below, identify the 3-dimensional figures that are used to create the composite figure.

Move the mouse cursor over the figure to check the answer.

Volume of Composite Figures

Finding the volume of a composites figure is like finding the volume of each solid figure. These individual solid figures such as prisms, cylinders, pyramids, cones, and spheres are combined with make three-dimensional solids called composites figures. There are two ways to find the volume of a composite figure:

Composite Figure: Stacked à one figure is stacked on top of each other

You need to find the volume of each figure and add them together

Composite Figure: Inside à one figure is inside the other figure

You need to find the volume of each figure and subtract them

Example A - Composite Figure - Stacked

Find the volume of the composite figure below.

Step 1 à Identify the three-dimensional solids in the figure above

The figure is a cone and a cylinder

Step 2 à Determine the volume of the cone and identify the formula of a volume of the cone.

V = 1/3 πr²h
Volume of a cone à 3215 ft³

Step 3 à Determine the volume of the cylinder and identify the formula of a volume of a cylinder

V = πr²h
Volume of a cylinder à 24,115 ft³

Step 4 à Find the sum of the cylinders

V cone + V cylinder
3215 ft³ + 24,115 ft³ = 27,330 ft³

Example B - Composite Figure: Inside

Find the volume of the composite figure.

The sphere is inside the cube.

Step 1 à Identify the three-dimensional solids in the figure above

The figure is a sphere and a cube

Step 2 à Determine the volume of the sphere and identify the formula of a volume of the sphere. (Remember that the radius is half of the diameter)

V = 4/3 πr³
268 in³

Step 3 à Determine the volume of the cube and identify the formula of a volume of a cube.

V = s³
(8 inches)³ = 512 in³

Step 4 à Find the differences in the volumes of both three-dimensional figures.

V sphere – V cube
512 in³ – 268 in³ = 244 in³

Click on the word volume to watch a presentation of composite figures.

Let's Practice - Volume of Composite Figures

1. Find the volume of the composite figure. (Stacked)

Move the mouse cursor over the figure to check the answer.

2. Find the volume of the composite figure. (Inside)

Move the mouse cursor over the figure to check the answer.

3. Find the volume of the composite figure. (Stacked)

Move the mouse cursor over the figure to check the answer.

4. Find the volume of the composite figure. (Inside)

Move the mouse cursor over the figure to check the answer.

Below are additional educational resources and activities for this unit.

Click on the icon to the left to view the steps of measuring the Volume of a Composite Figure.

Practice 1: Volume of a Composite Figure

Practice 2: Volume of a Composite Shape