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1. Regular hexagon, side length 14 cm

509.22 cm 2. ANSWER. Find the area of each polygon or circle. 1. Regular hexagon, side length 14 cm. EXAMPLE 1. Find the number of unit cubes. 3- D PUZZLE. Find the volume of the puzzle piece in cubic units. π 9 2 , or 81πft 2 . Use h = 6 ft to find the volume. EXAMPLE 2.

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1. Regular hexagon, side length 14 cm

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  1. 509.22 cm2 ANSWER Find the area of each polygon or circle. 1.Regular hexagon, side length14 cm

  2. EXAMPLE 1 Find the number of unit cubes 3- D PUZZLE Find the volume of the puzzle piece in cubic units.

  3. π 92, or 81πft2. Use h = 6 ft to find the volume. EXAMPLE 2 Find volumes of prisms and cylinders SOLUTION b. Right cylinder b. The area of the base is V = Bh = 81π(6) = 486π ≈ 1526.81 ft3

  4. EXAMPLE 3 Use volume of a prism ALGEBRA The volume of the cube is 90 cubic inches. Find the value of x. SOLUTION A side length of the cube is xinches. V = x3 Formula for volume of a cube 90 in3. = x3 Substitute for V. 4.48 in. ≈ x Find the cube root.

  5. ANSWER The volume of the puzzle cube is 7 units3 for Example 1,2,and 3 GUIDED PRACTICE 1. Find the volume of the puzzle piece shown in cubic units.

  6. ANSWER The volume of a square prism is 300 ft3 for Example 1,2,and 3 GUIDED PRACTICE 2. Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet.

  7. ANSWER The radius of a right cylinder is in 38 for Example 1,2,and 3 GUIDED PRACTICE 3. The volume of a right cylinder is 684π cubic inches and the height is 18 inches. Find the radius.

  8. EXAMPLE 4 Find the volume of an oblique cylinder Find the volume of the oblique cylinder. SOLUTION Cavalieri’s Principle allows you to use Theorem 12.7 to find the volume of the oblique cylinder. V = π r2h Formula for volume of a cylinder = π(42)(7) Substitute known values. = 112π Simplify.

  9. ANSWER The volume of the oblique cylinder is about 351.86cm3. EXAMPLE 4 Find the volume of an oblique cylinder ≈351.86 Use a calculator.

  10. EXAMPLE 5 Solve a real-world problem PLANTER The planter is made up of 13 beams. In centimeters, suppose the dimensions of each beam are 30 by 30 by 90. Find its volume.

  11. B = Area of large rectangle – 4 Area of small rectangle = 90 510 – 4(30 90) Solve a real-world problem EXAMPLE 5 SOLUTION The area of the base Bcan be found by subtracting the area of the small rectangles from the area of the large rectangle. = 35,100 cm2

  12. Solve a real-world problem EXAMPLE 5 Use the formula for the volume of a prism. V = Bh Formula for volume of a prism = 35,100(30) Substitute. = 1,053,000 cm3 Simplify. The volume of the planter is 1,053,000 cm3, or 1.053 m3.

  13. ANSWER The volume of the oblique prism is 180m3 for Example 4 and 5 GUIDED PRACTICE 4. Find the volume of the oblique prism shown below.

  14. ANSWER 205.81 ft3 for Example 4 and 5 GUIDED PRACTICE 5. Find the volume of the solid shown below.

  15. 1. Find the volume of the solid at the right. ANSWER 5437.5 in.3 3456 in.3 ANSWER Daily Homework Quiz 2. Find the volume of a right triangular prism with height 32 in., base height 12 in., and base length 18 in.

  16. ANSWER 4618.14 in.3 Daily Homework Quiz 3. Find the volume of a right cylinder with height 30 ftand diameter 14 ft. 4. A cylindrical beaker with diameter 10 in. and height 12 in. is filled with water that is then poured into a rectangular pan that is 14 in. by 9 in. by 3 in. What is the volume of each solid? Would the water overflow the pan? If so, what is the height of the water in the beaker after the pan is filled?

  17. ANSWER cylinder: 942.48 in.3; pan: 378 in.3; Yes, it would overflow the pan. After the pan is filled , the height of the water in the beaker will be about 7.2 in. Daily Homework Quiz

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