# 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 r*ectangular prism*, a *cylinder*, and a *square pyramid*.

**MATERIALS**

- Worksheet 3 Printable (PDF)
- Extension: Bonus Worksheet 3 Printable (PDF)
- Extension: Take-Home Activity 3 (PDF)
- Resource: Formula Chart (PDF)
- Resource: Mini-Poster (PDF)

**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) = *l* • *w* • *h*. 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 • *r2* • *h*. 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 • *r2* • *h*]. 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:

- Extension:
**Bonus Worksheet 3 Printable (PDF)** - Extension:
**Take-Home Activity 3 (PDF)**

**Program Links: **