A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.
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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.

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About This Lesson Plan



Setting the Stage with Geometry

Lesson 3: Volume of 3D Shapes


  • Grade 7–8: Geometry (CCSS 7.G.B.6 and 8.G.C.9)
  • Grades 6–8: Reason Abstractly and Quantitatively, Construct Viable Arguments, Use Appropriate Tools Strategically, and Look for and Attend to Precision (CCSS MP2, 3, 5, and 6); NCTM Geometry
  • Download a comprehensive Standards Chart


Students will be able to use formulas to measure the volume of a rectangular prism, a cylinder, and a square pyramid.


Introduction to Formulas for Finding Volume


Time Required: 30 minutes, plus additional time for worksheets

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. Using unifix cubes or a similar manipulative, construct a rectangular prism with height = 3 units, length = 4 units, and width = 5 units. Note: If you have enough time and an adequate supply of manipulatives, have students construct rectangular prisms, either individually or in groups.

2. Ask how many cubes it took to build the prism (60). So the prism's volume is 60 cubic units. Explain how a cubic unit is the unit of measure for volume. Stress the need for precision when indicating units of measure. If helpful, point out how the unit of measure for area is square units (unit times unit equals unit squared) and for volume is cubic units (unit times unit times unit equals unit cubed).

3. Ask students to find a relationship between the lengths of the sides and the volume. If necessary, show students the volume formula for rectangular prisms on the poster: V (volume) = l • w • h. Since the dimensions of the rectangular prism are 3 x 4 x 5, the volume equals 60 cubic units.

4. On the board, draw a cylinder with a radius of 3 feet and a height of 4 feet. Show students the volume formula for cylinders on the poster: V= π • r2h. Demonstrate how the volume of this cylinder is 113.04 cubic feet (3.14 x 32 x 4 = 113.04).

5. Finally, draw a square pyramid on the board with a base length of 6 feet and a base width of 6 feet. The height of the pyramid is 4 feet. Be sure to point out the difference between height and slant length, as students might confuse the two. Show students the volume formula for square pyramids on the poster:V= 1/3 BA h. Demonstrate that the volume of this pyramid is 48 cubic feet (1/3 • 36 • 4 = 48 cubic feet).

6. Guided Practice: In groups or in pairs, with use of calculators as an option, ask students to calculate the volume of:

  • A rectangular prism with length 6.5 meters, width 7 meters, and height 12.5 meters
  • A cylinder with a radius of 9 centimeters and height of 7.25 centimeters (use 3.14 for π and round to the nearest hundredth)
  • A square pyramid with a base side length of 12.5 inches and a height of 9 inches


Volume of the rectangular prism is 568.75 cubic meters (6.5 x 7 x 12.5)

Volume of the cylinder is 1,843.97 cubic centimeters (3.14 x 92 x 7.25)

Volume of the square pyramid is 468.75 cubic inches (1/3 x 12.5 x 12.5 x 9)

7. Independent Practice: Distribute Worksheet 3 Printable (PDF).

Check for Understanding: Go over all correct answers as a class referring to the Worksheet Answer Key (PDF).

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


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