WarmUp Exercises Find the area of each polygon

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Warm-Up Exercises Find the area of each polygon or circle. 1. Trapezoid, bases 12

Warm-Up Exercises Find the area of each polygon or circle. 1. Trapezoid, bases 12 ft and 18 ft, height 3 ft ANSWER 45 ft 2 2. Circle, diameter 8. 2 in. ANSWER 52. 81 in. 2

Warm-Up Exercises Find the area of each polygon or circle. 3. Regular hexagon, side

Warm-Up Exercises Find the area of each polygon or circle. 3. Regular hexagon, side length 14 cm ANSWER 509. 22 cm 2

Warm-Up 1 Exercises EXAMPLE Find the number of unit cubes 3 - D PUZZLE

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

Warm-Up 1 Exercises EXAMPLE Find the number of unit cubes SOLUTION To find the

Warm-Up 1 Exercises EXAMPLE Find the number of unit cubes SOLUTION To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows: The base is 7 units by 2 units. So, it contains 7. 2, or 14 unit cubes. The upper left box is 2 units by 2 units. So, it contains 2. 2, or 4 unit cubes. The upper right box is 1 unit by 2 units. So, it contains 1. 2, or 2 unit cubes. By the Volume Addition Postulate, the total volume of the puzzle piece is 14 + 2 = 20 cubic units.

Warm-Up 2 Exercises EXAMPLE Find volumes of prisms and cylinders Find the volume of

Warm-Up 2 Exercises EXAMPLE Find volumes of prisms and cylinders Find the volume of the solid. a. Right trapezoidal prism SOLUTION a. The area of a base is 1 (3)(6 + 14) = 30 cm 2 and h = 5 cm. 2 V = Bh = 30(5) = 150 cm 3

Warm-Up 2 Exercises EXAMPLE Find volumes of prisms and cylinders SOLUTION b. Right cylinder

Warm-Up 2 Exercises EXAMPLE Find volumes of prisms and cylinders SOLUTION b. Right cylinder b. The area of the base is π 92, or 81πft 2. Use h = 6 ft to find the volume. V = Bh = 81π(6) = 486π ≈ 1526. 81 ft 3

Warm-Up 3 Exercises EXAMPLE Use volume of a prism ALGEBRA The volume of the

Warm-Up 3 Exercises EXAMPLE 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.

Warm-Up Exercises GUIDED PRACTICE for Example 1, 2, and 3 1. Find the volume

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

Warm-Up Exercises GUIDED PRACTICE for Example 1, 2, and 3 2. Find the volume

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. ANSWER The volume of a square prism is 300 ft 3

Warm-Up Exercises GUIDED PRACTICE for Example 1, 2, and 3 3. The volume of

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. ANSWER The radius of a right cylinder is 38 in

Warm-Up 4 Exercises EXAMPLE Find the volume of an oblique cylinder Find the volume

Warm-Up 4 Exercises EXAMPLE 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 Formula for volume of a cylinder = π(42)(7) Substitute known values. = 112π Simplify.

Warm-Up 4 Exercises EXAMPLE Find the volume of an oblique cylinder ≈ 351. 86

Warm-Up 4 Exercises EXAMPLE Find the volume of an oblique cylinder ≈ 351. 86 Use a calculator. ANSWER The volume of the oblique cylinder is about 351. 86 cm 3.

Warm-Up 5 Exercises EXAMPLE Solve a real-world problem PLANTER The planter is made up

Warm-Up 5 Exercises EXAMPLE 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 90. Find its volume.

Solve a real-world problem Warm-Up 5 Exercises EXAMPLE SOLUTION The area of the base

Solve a real-world problem Warm-Up 5 Exercises EXAMPLE 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

Solve a real-world problem Warm-Up 5 Exercises EXAMPLE Use the formula for the volume

Solve a real-world problem Warm-Up 5 Exercises EXAMPLE 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.

Warm-Up Exercises GUIDED PRACTICE for Example 4 and 5 4. Find the volume of

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

Warm-Up Exercises GUIDED PRACTICE for Example 4 and 5 5. Find the volume of

Warm-Up Exercises GUIDED PRACTICE for Example 4 and 5 5. Find the volume of the solid shown below. ANSWER 205. 81 ft 3

Warm-Up Exercises Daily Homework Quiz 1. Find the volume of the solid at the

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

Warm-Up Exercises Daily Homework Quiz 3. Find the volume of a right cylinder with

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?

Warm-Up Exercises Daily Homework Quiz ANSWER cylinder: 942. 48 in. 3; pan: 378 in.

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.