Warm-Up Exercises

1. Regular hexagon, side length 14 cm

ANSWER 509.22 cm2

Find the area of each polygon or circle.

Warm-Up ExercisesEXAMPLE 1 Find the number of unit cubes

3- D PUZZLE Find the volume of the puzzle piece in cubic units.

Warm-Up ExercisesEXAMPLE 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 ft3

π 92, or 81πft2. Use h = 6 ft to find the volume.

Warm-Up ExercisesEXAMPLE 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 = x3

90 in3. = x3

4.48 in. ≈ x

Formula for volume of a cube

Substitute for V.

Find the cube root.

Warm-Up ExercisesGUIDED 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 units3

ANSWER

Warm-Up ExercisesGUIDED 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 ft3

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 1,2,and 3

3. The volume of a right cylinder is 684π cubicinches and the height is 18 inches. Find the radius.

The radius of a right cylinder is in 38

ANSWER

Warm-Up ExercisesEXAMPLE 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

= π(42)(7) Substitute known values.

= 112π Simplify.

Formula for volume of a cylinder

Warm-Up ExercisesEXAMPLE 4 Find the volume of an oblique cylinder

≈ 351.86 Use a calculator.

The volume of the oblique cylinder is about 351.86 cm3.

ANSWER

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesEXAMPLE 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 cm2

Warm-Up ExercisesEXAMPLE 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 cm3 Simplify.

The volume of the planter is 1,053,000 cm3, or 1.053 m3.

Warm-Up ExercisesGUIDED PRACTICE for Example 4 and 5

4. Find the volume of the oblique prism shown below.

The volume of the oblique prism is 180m3

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 4 and 5

5. Find the volume of the solid shown below.

ANSWER

205.81 ft3

Warm-Up ExercisesDaily 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 ExercisesDaily 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 ExercisesDaily 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 about7.2 in.