- Be able to use formulas to measure the volume of a rectangular prism, a cylinder, and a square pyramid
- Unifix Cubes or similar manipulative
- Setting the Stage With Geometry Worksheet: Pack it Up! What Will Fit? printable
- Setting the Stage With Geometry Reference Sheet: Perimeter, Area, Surface Area, and Volume printable
- Answer Key: Setting the Stage With Geometry printable
- Setting the Stage With Geometry Classroom Poster printable
- Optional: Setting the Stage With Geometry Take-Home Activity: The Perfect Fit printable
- Optional: Turn Up the Volume! Bonus Worksheet printable
- Make class sets of the Setting the Stage With Geometry Worksheet: Pack it Up! What Will Fit? printable and the Setting the Stage With Geometry Reference Sheet: Perimeter, Area, Surface Area, and Volume printable.
- Print a copy of the Answer Key: Setting the Stage With Geometry printable for your use.
- Hang a copy of the Setting the Stage With Geometry Classroom Poster printable in your classroom or project it using a computer and projector.
- Optional: Make class sets of the Setting the Stage With Geometry Take-Home Activity: The Perfect Fit printable and the Turn Up the Volume! Bonus Worksheet printable for students to complete as part of the Lesson Extensions.
Introduction to Formulas for Finding Volume
Step 1: Explain to your students that now that they've mastered measuring the surface area of 3-D shapes, they can move on to measuring volume, which is the amount of space inside a 3-D 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.
Step 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).
Step 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.
Step 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 • r2 • h. Demonstrate how the volume of this cylinder is 113.04 cubic feet (3.14 x 32 x 4 = 113.04).
Step 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).
Step 6: 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. Volume of the rectangular prism is 568.75 cubic meters (6.5 x 7 x 12.5)
- 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). Volume of the cylinder is 1,843.97 cubic centimeters (3.14 x 92 x 7.25)
- A square pyramid with a base side length of 12.5 inches and a height of 9 inches. Volume of the square pyramid is 468.75 cubic inches (1/3 x 12.5 x 12.5 x 9)
Step 7: Distribute the Setting the Stage With Geometry Worksheet: Pack it Up! What Will Fit? printable and have students complete the worksheet independently.
Step 8: Check for Understanding: Go over all correct answers as a class, referring to the Answer Key: Setting the Stage With Geometry printable.
Supporting All Learners
Provide the Setting the Stage With Geometry Reference Sheet: Perimeter, Area, Surface Area, and Volume printable for students who are having trouble remembering which formulas go with which polygon.
Use the following printables as extensions for this lesson:
- Setting the Stage With Geometry Take-Home Activity: The Perfect Fit printable
- Turn Up the Volume! Bonus Worksheet printable
- 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
For more information, download the comprehensive Standards Chart: Geometry printable.