A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.
What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk. Background photo: © Inga Nielsen/iStockphoto.
About This Lesson Plan

SUBJECT
Math, Geometry

GRADE
6-8

DURATION
20 Mins

COLLECTION
Setting the Stage with Geometry

Lesson 3: Volume of 3D Shapes

In this lesson, students build knowledge of volume, and complete worksheet problems related to calculating cargo space available for moving concert items.

OBJECTIVE
In “Pack It Up! What Will Fit?” students will understand formulas used to measure the volume of these basic three-dimensional shapes: a rectangular prism, a cylinder, and a square pyramid.

MATERIALS

DIRECTIONS
Time Required: 20 minutes, plus additional time for worksheets
Getting Started

1. Explain to your students that now that they’ve mastered measuring the surface area of 3D shapes, they can move on to measuring volume, which is the amount of space inside a 3D shape, measured in cubic units. Refer to the poster, which provides essential formulas.

2. Again, draw a rectangular prism on the board like the one from the Lesson 2 surface area unit with these measurements: height = 3 feet, length = 4 feet, and width = 5 feet.

3. Show students the volume formula for rectangular prisms on the poster: V (volume) = lwh. Ask students what the volume of the prism is. The answer is 4 • 5 • 3 = 60 cubic feet.

4. Now draw a cylinder again with the same dimensions as in Lesson 2: The radius is 3 feet and the height is 4 feet.

5. Show students the volume formula for cylinders on the poster: V = π • r2h. Ask students what the volume of the cylinder is when rounded to the nearest half foot. As 3.14 • 9 • 4 = 113.04 cubic feet, the answer is 113 cubic feet.

6. You might add that a cylinder is like a barrel, and volume measurement can help determine how much liquid will fit in a container this size. One cubic foot = 7.48 gallons. Ask students how much water this cylinder would hold. The answer is 7.48 • 113.04, or 845.54 gallons (when rounded to the nearest hundredth). Students may need a calculator to solve this problem.

7. Finally, draw a square pyramid on the board with the same dimensions as in Lesson 2: The square pyramid has a base length of 6 feet and a base width of 6 feet. The height of the pyramid is 4 feet.

8. Show students the volume formula for square pyramids on the poster: V = 1/3 • BA • h. Ask students for the volume of the square pyramid. The answer is 1/3 • 36 • 4 = 48 cubic feet.

9. Distribute Worksheet 3 Printable (PDF). Tell students they should complete all the questions. You may want to take some extra time to go over the bonus question, which introduces the formula for the volume of a cone [V = π • 1/3 • r2h]. Go over all correct answers as a class referring to the Worksheet Answer Key (PDF).

10. Use the following printables as extensions to Lesson 3:

 

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