Preview Warm Up California Standards Lesson Presentation

Warm Up Find the area of each figure. Use 3.14 as an estimate for . 1. rectangle with base length 8 in. and height 12 in. 96 in2 2. circle with diameter 8 ft 50.24 ft2

MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Also covered: AF3.1, AF3.2 California Standards

Vocabulary volume

Volume is the number of cubic units needed to fill a space.

You need 10, or 5 · 2, centimeter cubes to cover the bottom of this rectangular prism. You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes.

Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cubic centimeters, or 30 cm3.

The volume of a rectangular prism is the area of its base times its height. This formula can be used to find the volume of any prism.

The height of a prism is the distance between its two bases. Caution!

Additional Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. Step 1: Find the area of the base. 13 in. 11 in. 26 in. B = 26 · 11 The base is a rectangle. B = 286 Multiply.

Additional Example 1 Continued Find the volume of the rectangular prism. Step 2: Find the volume. 13 in. 11 in. 26 in. V = Bh Write the formula. V = 286 • 13 Substitute for B and h. V = 3,718 in3 Multiply. The volume of the prism is 3,718 in3.

Additional Example 2: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. A. Step 1: Find the area of the base. B = ( • 3.9 • 1.3) 1 2 __ The base is a triangle. B = 2.535 Multiply.

Additional Example 2: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. A. Step 2: Find the volume. V = Bh Write the formula. V = 2.535 • 4 Substitute for B and h. V = 10.14 m3 Multiply. The volume of the prism is 10.14 m3.

Additional Example 3: Application An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain. 5.2 cm 3 cm Step 1: Find the area of the base. 6 cm B = • 6 • 5.2 = 15.6 1 2 __ The base is a triangle.

Additional Example 3 Continued An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain. 5.2 cm 3 cm Step 2: Find the volume. 6 cm V = Bh Write the formula. V = 15.6 • 3 = 46.8 cm3 Substitute for B and h. No; each paperweight will require about 47 cm3 of glass.

Find the volume of the rectangular prism. Check It Out! Example 1 Find the volume of the rectangular prism. Step 1: Find the area of the base. 16 in. 12 in. 29 in. B = 29 · 12 The base is a rectangle. B = 348 Multiply.

Check It Out! Example 1 Continued Find the volume of the rectangular prism. Step 2: Find the volume. 16 in. 12 in. 29 in. V = Bh Write the formula. V = 348 • 16 Substitute for B and h. V = 5,568 in3 Multiply. The volume of the prism is 5,568 in3.

Check It Out! Example 2 Find the volume of each triangular prism. A. Step 1: Find the area of the base. 7 m 1.6 m 4.2 m B = ( • 4.2 • 1.6) 1 2 __ The base is a triangle. B = 3.36 Multiply.

Find the volume of each triangular prism. Check It Out! Example 2 Find the volume of each triangular prism. A. Step 2: Find the volume. 7 m 1.6 m 4.2 m V = Bh Write the formula. V = 3.36 • 7 Substitute for B and h. V = 23.52 m3 Multiply. The volume of the prism is 23.52 m3.

Step 1: Find the area of the base. Check It Out! Example 3 An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain. 5.5 cm 5 cm Step 1: Find the area of the base. 6 cm B = • 6 • 5.5 = 16.5 1 2 __ The base is a triangle.

Check It Out! Example 3 Continued An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain. 5.5 cm 5 cm Step 2: Find the volume. 6 cm V = Bh Write the formula. V = 16.5 • 5 = 82.5 cm3 Substitute for B and h. No; each building will require about 83 cm3 of paper.

Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm 2. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm 3. Find the volume of the figure shown. 3,600 cm3 153.3 cm3 38.13 cm3