1. Warm-Up Exercises 1. Regular hexagon, side length 14 cm ANSWER 509.22 cm 2 Find the area of each polygon or circle.

2. Warm-Up Exercises EXAMPLE 1 Find the number of unit cubes 3- D PUZZLEFind the volume of the puzzle piece in cubic units.

3. Warm-Up Exercises EXAMPLE 2 Find volumes of prisms and cylinders b. Right cylinder SOLUTION b. The area of the base is V = Bh = 81π(6) = 486π ≈ 1526.81 ft 3 π 9 2, or 81πft 2. Use h = 6 ft to find the volume.

4. Warm-Up Exercises 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 x inches. V = x 3 90 in 3. = x 3 4.48 in. ≈ x Formula for volume of a cube Substitute for V. Find the cube root.

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

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

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

8. Warm-Up Exercises 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 r 2 h = π(4 2 )(7) Substitute known values. = 112π Simplify. Formula for volume of a cylinder

9. Warm-Up Exercises EXAMPLE 4 Find the volume of an oblique cylinder ≈ 351.86 Use a calculator. The volume of the oblique cylinder is about 351.86 cm 3. ANSWER

10. Warm-Up Exercises EXAMPLE 5 Solve a real-world problem PLANTERThe 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. Warm-Up Exercises EXAMPLE 5 Solve a real-world problem SOLUTION The area of the base B can be found by subtracting the area of the small rectangles from the area of the large rectangle. B = Area of large rectangle – 4 Area of small rectangle = 90 510 – 4(30 90) = 35,100 cm 2

12. Warm-Up Exercises EXAMPLE 5 Solve a real-world problem Use the formula for the volume of a prism. V = Bh Formula for volume of a prism = 35,100(30) Substitute. = 1,053,000 cm 3 Simplify. The volume of the planter is 1,053,000 cm 3, or 1.053 m 3.

13. Warm-Up Exercises GUIDED PRACTICE for Example 4 and 5 4. Find the volume of the oblique prism shown below. The volume of the oblique prism is 180m 3 ANSWER

14. Warm-Up Exercises GUIDED PRACTICE for Example 4 and 5 5. Find the volume of the solid shown below. ANSWER 205.81 ft 3

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

16. Warm-Up Exercises Daily Homework Quiz 3. Find the volume of a right cylinder with height 30 ft and diameter 14 ft. ANSWER 4618.14 in. 3 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. Warm-Up Exercises Daily Homework Quiz 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.