Finding Volume
Finding Volume
Today you will
 Review how to apply the Associative Property
of Multiplication to multiply three numbers.  Use unit cubes to find volume.
 Apply the volume formula to find the volume of rectangular prisms.
 Solve realworld problems using volume.
Finding Volume
Multiply 5 × 3 × 4.
5 × 3 × 4
5 × 3 × 4
15 × 4
60
Finding Volume
Multiply 12 × 8 × 5.
12×8×5
12×8×5
12× 40
480
Finding Volume
Multiply 7 × 5 × 3.
7×5×3
7×5×3
7×
Good job! 7 × 5 × 3 = 105
Congratulations!
You have earned a castle for the aquarium.
7 × 5 × 3
First, multiply 5 times 3.
7 × 15
Then multiply 7 times 15.
105
HINTMultiply two numbers. Then multiply the third number.
Finding Volume
Select each term to learn more about it.
A rectangular prism is a solid object with 6 rectangular faces and a
length, width, and height.
length, width, and height.
height
width
length
The volume of a solid figure is the amount of space the figure takes up, or the amount of space inside the figure.
Finding Volume
Unit Cube
A unit cube is a rectangular prism that has a length, width, and height of
one unit, such as one inch or one centimeter.
one unit, such as one inch or one centimeter.
1 unit
1 unit
1 unit
volume = 1 cubic unit
Since the length, width, and height are all the same, all the sides of the unit cube are squares that are the same size.
Finding Volume
The volume of a rectangular prism equals the number of unit cubes it takes to fill its space.
volume = unit cubes
Finding Volume
Find the number of unit cubes inside the rectangular prism.
one layer = unit cubes
number of layers =
The rectangular prism is filled
with unit cubes.
with unit cubes.
Good job! The rectangular prism is filled with 24 unit cubes.
Congratulations!
You have earned a plant for the aquarium.
Each layer has
8 unit cubes.
There are 3 layers.
8 x 3 = 24
HINTMultiply the number of unit cubes in one layer by the number of layers.
Finding Volume
How can you write a formula for finding the
number of unit cubes in one layer of the
rectangular prism using the terms length and
width? Type your answer in the box.
number of unit cubes in one layer of the
rectangular prism using the terms length and
width? Type your answer in the box.
layer 1
layer 2
layer 3
one layer = 8 unit cubes
Finding Volume
The measurements for the length, width, and height of a rectangular prism represent the number of unit cubes along each edge.
height = 8 unit cubes
width = 3 unit cubes
length = 2 unit cubes
Finding Volume
8 unit cubes
3 unit cubes
2 unit cubes
volume =
unit cubes in one layer
number of layers
The equation for
volume is
length × width × height.
HINTRecall how the number of cubes in one layer relates to the length and width.
Finding Volume
8 unit cubes
3 unit cubes
2 unit cubes
volume =
length ×
width ×
height
volume =
2 units is the length,
3 units is the width,
8 units is the height.
Then volume formula
should read
2 units x 3 units x 8 units.
HINTReview the dimensions of a rectangular prism.
Finding Volume
8 unit cubes
3 unit cubes
2 unit cubes
13
24
48
72
volume = 2 unit cubes × 3 unit cubes × 8 unit cubes
The volume of the rectangular prism is unit cubes.
Correct!
The volume is 48 unit cubes.
Congratulations!
You have earned a scuba diver for the aquarium.
HINTMultiply two numbers. Then multiply the third number.
The volume of the
rectangular prism
is 48 unit cubes.
2 x 3 x 8 = 48
Finding Volume
The bottom side of a rectangular prism is a rectangle called the base (B). The area of a rectangle is its length times its width. What is another possible formula for the volume of a rectangular prism using V, B, and h?
h
w
l
B
Finding Volume
Find the volume of the rectangular prism.
6 units
3 units
3 units
3
6
3
V=l ×w ×h
V=
V= ×
V=
HINTMultiply two numbers. Then multiply the third number.
3 x 3 = 9
9 x 6 = 54 cubic units
Finding Volume
Find the volume of the rectangular prism.
V=l × w × h
V=7 × × 4
V=7 ×
V=cubic cm
Correct! The volume is 56 cubic centimeters.
Congratulations!
You have earned a regal angelfish for the aquarium.
HINTMultiply the length, width, and height to find the volume of the rectangular prism. Multiply two numbers and then multiply by the third number.
The width is 2 cm.
When 2 is multiplied by 4,
the product is 8.
7 is then multiplied by 8.
7 x 8 = 56
Finding Volume
Find the volume of each prism.
A
B
20 cm
10 cm
14 cm
10 cm
7 cm
40 cm
V = l × w × h
V = × ×
V = ×
V = cubic cm
V = l × w × h
V = × ×
V = ×
V = cubic cm
HINT Remember to multiply two of the numbers first and then multiply the third number.
Possible Solution
V = 14 × 10 × 20
V = 140 x 20
V = 2,800 cubic cm
V = 40 × 7 x 10
V = 280 × 10
V = 2,800 cubic cm
Congratulations!
You have earned a threadfin butterflyfish for the aquarium.
Finding Volume
A
20 cm
10 cm
14 cm
B
10 cm
7 cm
40 cm
Use the prisms from the previous problem. What is another way to arrange the 2,800 cubes to form a rectangular prism? How does the volume of this prism compare to the volume of the ones shown? Explain your reasoning.
Finding Volume
Select the rectangular prisms that have the same volume.
A
A
B
B
C
C
8 in.
1 in.
5 in.
10 in.
4 in.
1 in.
6 in.
5 in.
1 in.
Type your explanation in the box:
The volume of a prism A
is 40 cubic inches because
is 40 cubic inches because
5 × 1 × 8 = 40 cubic inches.
The volume of a prism B
is 40 cubic inches because
is 40 cubic inches because
10 × 1 × 4 = 40 cubic inches.
Both prisms A and B have a
volume of 40 cubic inches.
volume of 40 cubic inches.
Correct! Prisms A and B both have a volume of 40 cubic inches.
Congratulations!
You have earned a pufferfish for the aquarium.
HINT Use the formula V = l × w × h to find the volume of each rectangular prism.
Finding Volume
If the sides of prism B from the previous problem
were measured in centimeters instead of inches,
how would the actual volumes of A and B compare?
How would the numbers representing the two
volumes compare? Explain your reasoning.
were measured in centimeters instead of inches,
how would the actual volumes of A and B compare?
How would the numbers representing the two
volumes compare? Explain your reasoning.
A
B
8 in.
1 in.
5 in.
h cm
w cm
l cm
Finding Volume
Click to highlight the information needed to solve the problem.
Your doctors’ office wants a new aquarium for the waiting room. The space for
the aquarium is 60 inches long, 24 inches wide, and 48 inches high. What is
the volume of the space available for the aquarium?
the aquarium is 60 inches long, 24 inches wide, and 48 inches high. What is
the volume of the space available for the aquarium?
60 in.
24 in.
48 in.
The measurements
for the space for the
aquarium are needed
to solve the problem.
for the space for the
aquarium are needed
to solve the problem.
Great job! To find the volume of the aquarium, you need the length, width, and height.
Congratulations!
You have earned a clownfish for the aquarium.
HINT Think about what you need to find the volume.
What information in the problem will you need to use?
What information in the problem will you need to use?
Finding Volume
60 in.
24 in.
48 in.
Fill in the blank.
The volume of the space for the aquarium is cubic inches.
Explain how you found the answer.
Great job! The space for the aquarium is 69,120 cubic inches.
Congratulations!
You have earned a powder blue tang for the aquarium.
The volume of the
space for the aquarium is 69,120 cubic inches.
space for the aquarium is 69,120 cubic inches.
60 × 24 × 48 = 69,120
HINT Use the formula V = l × w × h to find the volume of the rectangular prism aquarium.
Finding Volume
One gallon of water has a volume of 231 cubic inches. Which size of aquarium should
be bought for the doctor’s waiting room? Round your answer to select the best size.
be bought for the doctor’s waiting room? Round your answer to select the best size.
69,120 cubic inches ÷ 231 cubic inches ≈ 299 gallons.
The tank needs to be 300 gallons.
The tank needs to be 300 gallons.
60 in.
24 in.
48 in.
Great job! The doctor should
buy a 300gallon aquarium.
buy a 300gallon aquarium.
Congratulations!
You have earned a mandarinfish for the aquarium.
HINTThere are 231 cubic inches in 1 gallon of water.
Finding Volume
Drag and drop the items you have earned for the aquarium into the tank. When you are finished, click the NEXT arrow.
Finding Volume
Reflect by responding to one of the questions below.
How can you use what you have learned in your daily life?
Type your response in the box.
What questions do you still have?
Type your response in the box.
Finding Volume
Extend the Learning! Answer the questions below to explore further.
The doctors plan to cover the bottom of
the aquarium with gravel. They want the
gravel to be 2 inches high. In cubic inches,
what is the volume of gravel needed?
the aquarium with gravel. They want the
gravel to be 2 inches high. In cubic inches,
what is the volume of gravel needed?
Type your answer in the box.
cubic inches
cubic inches
60 in.
24 in.
48 in.
2 in.
Explain how finding the volume of the gravel
is different from finding the volume of the
tank for the aquarium
is different from finding the volume of the
tank for the aquarium
Type your response in the box.
Finding Volume
Extend the Learning! Answer the questions below to explore further.
In addition to adding 2 inches of gravel to the bottom, the doctors will fill the tank with water until the
water is 4 inches from the top. How many cubic inches of water is needed? How many gallons? Remember,
1 gallon of water equals 231 cubic inches.
water is 4 inches from the top. How many cubic inches of water is needed? How many gallons? Remember,
1 gallon of water equals 231 cubic inches.
The volume of water in the tank will be cubic inches,
or about gallons.
or about gallons.
Explain how you found the answer.
Finding Volume
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