Volume is the sixth of seven self-paced lessons in the “Perimeter, Area, and Volume” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson focuses on finding the volume of a solid figure.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, students will apply their understanding of the capacity of solid figures to solving problems.

They will need to find the volume of an object by using a provided formula.

They also need to know how to solve for a “missing” dimension when the volume is given.

This lesson focuses on finding the volume of a solid figure. On the GED Mathematics Test, students need to recognize a three-dimensional figure that is set in a realistic context and select the correct formula from the formulas page. An additional challenge for students is, when given the volume of a figure, to find a missing dimension.

Note: Based on the GED formulas page, use the value of π in the decimal form, 3.14.

2Volume

Watch the video for an explanation of finding the volume of a shape.

Finding Volume

Video: 2m 11s

Volume is the measure of how much space there is within a three-dimensional object (an object with length, width, and height). The answer to a volume problem is shown in cubic units.

Formulas for finding the volume of some objects are included on the GED formulas page, which will be provided to students when they take the test. To find volume, first identify the shape. Then choose the formula and substitute any given measures to solve.

Question Maurice is planning to buy an air conditioner for his bedroom. He will need to know the volume of his room in cubic feet. Each of the room’s three dimensions measures 12 feet. What is the volume of the room in cubic feet?

Step 1 Determine the shape of the room—its dimensions are 12 ft by 12 ft by 12 ft. Then choose the formula for a cube because all of the dimensions are the same.

cube Volume = edge^{3}

Step 2 Substitute 12 ft for edge in the formula and solve.

Volume = edge^{3}

= 12^{3}

= 12 × 12 × 12

= 1,728

Answer 1,728 cubic feet

3Finding a Missing Dimension

Some math problems will include the volume of an object but not one of its dimensions.

Instead of solving for volume, use a volume formula to solve for the “missing” dimension. Substitute any given measures into the formula and solve for the unknown dimension.

Question The volume of the storage container shown below is 3,500 cubic feet. What is the length of the container in feet?

Step 1 Determine the shape of the container. Then, identify the shape based on the picture and find the formula for a rectangular solid on the GED formulas page.

Step 2 Place the given volume, width, and height measurements into the formula, and solve.

Volume = length × width × height

3,500 = / × 14 × 10

3,500 = / × 140

3,500 ÷ 140 = / × 140÷ 140 ←divide both sides by 140 to solve for /

25 = length

Answer 25 feet

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, consider how you would work through them with your students.

How could you help students see that Question 2 is a missing dimension problem?

In this lesson you have learned about area. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.

Assign directly to your students using the code or link above, without having them log in. Simply tell your students to go to
www.pbsstudents.org and enter the Assignment Code, or click on the Assignment URL to share the assignment as a link.