Learn to find the volume of prisms and Pyramids

1. Learn to find the volume of prisms and Pyramids

2. Vocabulary volume

3. Any three-dimensional figure can be filled completely with congruent cubes and parts of cubes. The volumeof a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

4. Additional Example 1: Using Cubes to Find the Volume of a Rectangular Prism Find how many cubes the prism holds. Then give the prism’s volume. You can find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. 1 · 4 · 3 = 12 There are 12 cubes in the prism, so the volume is 12 cubic units.

5. 1 cm 3 cm 4 cm To find a prism’s volume, multiply its length by its width by its height. 4 cm · 3 cm · 1cm = 12 cm3 length · width · height = volume area of base · height = volume

6. Reading Math Any unit of measurement with an exponent of 3 is a cubic unit. For example, cm3 means “cubic centimeter” and in3 means “cubic inch.”

7. Check It Out: Example 1 Find how many cubes the prism holds. Then give the prism’s volume. You can find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. 2 · 4 · 3 = 24 There are 24 cubes in the prism, so the volume is 24 cubic units.

8. 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.

9. Additional Example 2A: Using a Formula to Find the Volume of a Prism Find the volume of the prism. 4 ft 4 ft 12 ft V = Bh Use the formula. The bases are rectangles. The area of each rectangular base is 12 · 4 = 48 V = 48· 4 Substitute for B and h. Multiply. V = 192 The volume of the prism is 192 ft3.

10. 1 2 The base is · 3 · 4 = 6 Additional Example 2B: Using a Formula to Find the Volume of a Prism Find the volume of the prism. V = Bh Use the formula. The base is a triangle. V = 6· 6 Substitute for B and h. Multiply. V = 36 The volume of the prism is 36 cm3.

11. Check It Out: Example 2A Find the volume of the prism. 6 ft 6 ft 8 ft V = Bh Use the formula. The bases are rectangles. The area of each rectangular base is 8 · 6 = 48 V = 48· 6 Substitute for B and h. Multiply. V = 288 The volume to the nearest tenth is 288 ft3.

12. 1 2 The base is · 1.5 · 5 = 3.75 Check It Out: Example 2B Find the volume of the prism. 5 in 4 in. 1.5 in. V = Bh Use the formula. The base is a triangle. V = 3.75· 4 Substitute for B and h. Multiply. V = 15 The volume of the prism is 15 in3.

13. 10-3 Volume of Pyramids Course 2 In fact, the volume of a pyramid is exactly one-third the volume of a prism if they have the same height and same-size base. The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex.

14. 10-3 Volume of Pyramids Course 2 Additional Example 1: Finding the Volume of a Rectangular Pyramid Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3 V = Bh Use the formula. 4 ft Find the area of the rectangular base. B = 5 · 7 = 35 1 3 V = · 35 · 4 Substitute for B and h. 7 ft 5 ft Multiply. V ≈ 46.7 ft3 1 3 V = Round the measurements. · 30 · 5 Estimate The answer is reasonable. V = 50 ft3

15. Check It Out: Example 1 Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3 V = Bh Use the formula. 4 ft Find the area of the rectangular base. B = 8 · 7 = 56 1 3 V = · 56 · 4 Substitute for B and h. 7 ft 8 ft Multiply. V ≈ 74.7 ft3 1 3 V = Estimate Round the measurements. · 60 · 4 The answer is reasonable. V = 80 ft3

16. Lesson Quiz: Part I Find how many cubes the prism holds. Then give the prisms volume. 1. 2. 48 cubic units 792 cm3