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Warm-Up Exercises
Find the area of each polygon or circle.
1. Regular hexagon, side length 14 cm
ANSWER
509.22 cm2
Warm-Up1Exercises
EXAMPLE
Find the number of unit cubes
3- D PUZZLE Find the volume of the puzzle piece
in cubic units.
Warm-Up2Exercises
EXAMPLE
Find volumes of prisms and cylinders
SOLUTION
b. Right cylinder
b. The area of the base is
π 92, or 81πft2. Use h = 6 ft to find the volume.
V = Bh = 81π(6) = 486π ≈ 1526.81 ft3
Warm-Up3Exercises
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 = x3
90 in3. = x3
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 of the puzzle
piece shown in cubic units.
ANSWER
The volume of the puzzle cube is 7 units3
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 ft3
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-Up4Exercises
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 r2 h
Formula for volume of a cylinder
= π(42)(7)
Substitute known values.
= 112π
Simplify.
Warm-Up4Exercises
EXAMPLE
Find the volume of an oblique cylinder
≈ 351.86
Use a calculator.
ANSWER
The volume of the oblique cylinder is about
351.86 cm3.
Warm-Up5Exercises
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 30
by 90. Find its volume.
Solve a real-world problem
Warm-Up5Exercises
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 cm2
Solve a real-world problem
Warm-Up5Exercises
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 cm3
Simplify.
The volume of the planter is 1,053,000 cm3, or
1.053 m3.
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 180m3
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4 and 5
5. Find the volume of the solid shown below.
ANSWER
205.81 ft3
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
Find the volume of a right cylinder with height
30 ft and diameter 14 ft.
3.
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.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.