1. Holt CA Course 1 10-8 Volume of Prisms 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

2. Holt CA Course 1 10-8 Volume of Prisms Vocabulary Volume Volume of Prisms Formula

3. Holt CA Course 1 10-8 Volume of Prisms Volume is the number of cubic units needed to fill a space.

4. Holt CA Course 1 10-8 Volume of Prisms 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.

5. Holt CA Course 1 10-8 Volume of Prisms Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cubic centimeters, or 30 cm 3.

6. Holt CA Course 1 10-8 Volume of Prisms 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.

7. Holt CA Course 1 10-8 Volume of Prisms Teacher Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. B = 26 · 11 The base is a rectangle. Multiply.B = 286 13 in. 26 in. 11 in. Step 1: Find the area of the base.

8. Holt CA Course 1 10-8 Volume of Prisms Teacher Example 1 Continued: Find the volume of the rectangular prism. V = Bh Write the formula. V = 286 13Substitute for B and h. Multiply.V = 3,718 in 3 13 in. 26 in. 11 in. Step 2: Find the volume. The volume of the prism is 3,718 in 3.

9. Holt CA Course 1 10-8 Volume of Prisms Student Practice 1: Find the volume of the rectangular prism. B = 29 · 12 The base is a rectangle. Multiply.B = 348 Step 1: Find the area of the base. 16 in. 29 in. 12 in.

10. Holt CA Course 1 10-8 Volume of Prisms Student Practice 1 Continued: Find the volume of the rectangular prism. V = Bh Write the formula. V = 348 16Substitute for B and h. Multiply.V = 5,568 in 3 Step 2: Find the volume. The volume of the prism is 5,568 in 3. 16 in. 29 in. 12 in.

11. Holt CA Course 1 10-8 Volume of Prisms You can also use the formula V= Bh to find the volume of a triangular prism. For triangular prisms, B represents the area of a triangle, rather than a rectangle.

12. Holt CA Course 1 10-8 Volume of Prisms Teacher 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. The base is a triangle. B = ( 3.9 1.3) 1 2 __ Multiply.B = 2.535

13. Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2A: Finding the Volume of a Triangular Prism Continued Find the volume of each triangular prism. A. Step 2: Find the volume. V = BhWrite the formula. V = 2.535 4 Substitute for B and h. Multiply.V = 10.14 m 3 The volume of the prism is 10.14 m 3.

14. Holt CA Course 1 10-8 Volume of Prisms The height of a prism is the distance between its two bases. Caution!

15. Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2B: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. B. Step 1: Find the area of the base. The base is a triangle. B = ( 6.5 7) 1 2 __ Multiply.B = 22.75

16. Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2B: Finding the Volume of a Triangular Prism Continued Find the volume of each triangular prism. B. Step 2: Find the volume. V = BhWrite the formula. V = 22.75 6 Substitute for B and h. Multiply.V = 136.5 ft 3 The volume of the prism is 136.5 ft 3.

17. Holt CA Course 1 10-8 Volume of Prisms Student Practice 2A: Find the volume of each triangular prism. A. Step 1: Find the area of the base. The base is a triangle. B = ( 4.2 1.6) 1 2 __ Multiply.B = 3.36 1.6 m 7 m 4.2 m

18. Holt CA Course 1 10-8 Volume of Prisms Student Practice 2A Continued: Find the volume of each triangular prism. A. Step 2: Find the volume. V = BhWrite the formula. V = 3.36 7 Substitute for B and h. Multiply.V = 23.52 m 3 The volume of the prism is 23.52 m 3. 1.6 m 7 m 4.2 m

19. Holt CA Course 1 10-8 Volume of Prisms Student Practice 2B: Find the volume of each triangular prism. B. Step 1: Find the area of the base. The base is a triangle. B = ( 4.5 9) 1 2 __ Multiply.B = 20.25 4.5 ft 5 ft 9 ft

20. Holt CA Course 1 10-8 Volume of Prisms Student Practice 2B Continued: Find the volume of each triangular prism. B. Step 2: Find the volume. V = BhWrite the formula. V = 20.25 5 Substitute for B and h. Multiply.V = 101.25 ft 3 The volume of the prism is 101.25 ft 3. 4.5 ft 5 ft 9 ft

21. Holt CA Course 1 10-8 Volume of Prisms Teacher 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. Step 1: Find the area of the base. The base is a triangle. B = 6 5.2 = 15.6 1 2 __ 5.2 cm 6 cm 3 cm

22. Holt CA Course 1 10-8 Volume of Prisms Teacher 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. Step 2: Find the volume. 5.2 cm 6 cm 3 cm V = BhWrite the formula. V = 15.6 3 = 46.8 cm 3 Substitute for B and h. No; each paperweight will require about 47 cm 3 of glass.

23. Holt CA Course 1 10-8 Volume of Prisms Student Practice 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. Step 1: Find the area of the base. The base is a triangle. B = 6 5.5 = 16.5 1 2 __ 5.5 cm 6 cm 5 cm

24. Holt CA Course 1 10-8 Volume of Prisms Step 2: Find the volume. V = BhWrite the formula. V = 16.5 5 = 82.5 cm 3 Substitute for B and h. No; each building will require about 83 cm 3 of paper. 5.5 cm 6 cm 5 cm Student Practice 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.

25. Holt CA Course 1 10-8 Volume of Prisms 10.8 Warm-Up Find the volume of each figure. 1. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm 2. Find the volume of the figure shown.