All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 12 Lesson 9 Volume of Prisms will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 12 Lesson 9 Volume of Prisms
Volume is the amount of space inside a three-dimensional figure. You can use either formula below to find the volume of a prism.
Common units of volume are cubic inches, cubic feet, cubic yards, cubic centimeters, and cubic meters.
Math in My World
Example 1
On his family vacation to the beach, Armando filled a cooler with water and snacks. Find the volume of the cooler.
One Way
Use V = l × w × h.
V = l × w × h Volume formula
l = 30, w = 15, h = 20
V = __________ × ___________ × ____________
Multiply
V = ______________
Another Way
Use V = B × h.
V = B × h Volume formula
B = 30 × 15, h = 20
V = __________ × ___________
Multiply
V = ______________
Answer:
One way:
The above-given dimensions:
l = 30, w = 15, h = 20
We know that the formula for the volume of the rectangular prism:
V = length x width x height
V = 30 x 15 x 20
V = 9000
Therefore, the volume of the prism is 9000 cubic inches.
Second way:
Volume = base area x height
base area = 30 x 15 = 450
we know height = 20
Now substitute the values in the formula:
V = 450 x 20
V = 9000.
Therefore, the volume of the cooler is 9000 cubic inches.
Example 2
Find the volume of the prism.
V= l × w × h Volume formula
V= 17 × 7 × 9
V = __________ × (___________ × __________) Associative Property
V = ____________ × ____________ Multiply.
V = ____________ Multiply
The volume,of the prism is ______________ cm3.
Answer:
The formula is given above.
The dimensions are given.
V = 17 x 7 x 9
V = 17 x ( 7 x 9 )
V = 17 x 63
V = 1071
Therefore, the volume of the prism is 1071 cubic centimetres.
Guided Practice
Find the volume of each prism.
Question 1.
V = l × w × h
V = ___________ × ____________ × ____________
V = _____________ mm3
Answer:
The above dimensions:
length = 11; width = 7; height = 9
The volume of the rectangular prism = length x width x height
V = 11 x 7 x 9
V = 663
Therefore, the volume of the prism is 663 cubic millimetres.
Question 2.
V = B × h
V = ___________ × ___________
V = ____________ ft3
Answer:
The above-given:
the base area given that is 24 square feet
height = 12 feet
Now substitute these values in the formula:
The volume of the prism = base area x height
V = 24 x 12
V = 288
Therefore, the volume of the prism is 288 cubic feet.
Talk Math
If you know the area of the base of a rectangular prism and the prism’s height, which formula would you use? Why?
Answer:
The base of the prism is always rectangular, so the area is length x width. As it was a 3D figure, height is also given. So finally, we use the formula to calculate volume is:
The volume of the rectangular prism = base area x height
where base area = length x width.
Independent Practice
Mathematical PRACTICE Use Symbols Find the volume of each prism. Use the formula V = l × w × h or V = B × h.
Question 3.
V = ______________
Answer:
The above-given dimensions:
length = 4 inches; width = 2 inches; height = 3 inches
We know that the volume of the rectangular prism formula
V = length x width x height
V = 4 x 2 x 3
V = 24
Therefore, the volume of the prism is 24 cubic inches.
Question 4.
V = ______________
Answer:
The above dimensions:
length = 26; width = 12; height = 3
The volume of the rectangular prism = length x width x height
V = 26 x 12 x 3
V = 936
Therefore, the volume of the prism is 936 cubic centimetres.
Question 5.
V = ______________
Answer:
The above dimensions:
length = 11; width = 11; height = 11
The volume of the rectangular prism = length x width x height
V = 11 x 11 x 11
V = 1331
Therefore, the volume of the prism is 1331 cubic inches.
Question 6.
V = ______________
Answer:
The above dimensions:
length = 23; width = 9; height = 16
The volume of the rectangular prism = length x width x height
V = 23 x 9 x 16
V = 3312
Therefore, the volume of the prism is 3312 cubic metres.
Question 7.
V = ______________
Answer:
The above dimensions:
base area = 108; height = 9
The volume of the rectangular prism = base area x height
V = 108 x 9
V = 972
Therefore, the volume of the prism is 972 cubic centimetres.
Question 8.
V = ______________
Answer:
The above dimensions:
base area = 90; height = 11
The volume of the rectangular prism = base area x height
V = 90 x 11
V = 990
Therefore, the volume of the prism is 990 cubic feet.
Problem Solving
Question 9.
Find the volume of the Frog Queen building in Graz, Austria. The building is 18 meters long, 17 meters tall, and 18 meters wide.
Answer:
The above-given:
The length of the building in metres = 18
The height of the building in metres = 17
The width of the building in metres = 18
The above dimensions:
The volume of the rectangular prism = length x width x height
V = 18 x 18 x 17
V = 5508
Therefore, the volume of the prism is 5508 cubic metres.
Question 10.
Mathematical PRACTICE Model Math Two pet carriers are in the shape of rectangular prisms. Determine the volume of each pet carrier. Circle the carrier that has the greater volume.
Land Carrier: _____________ in3
Olympic Carrier: _____________ in3
Answer:
The above-given dimensions for the land carrier:
The above dimensions:
length = 20; width = 12; height = 12
The volume of the rectangular prism = length x width x height
V = 20 x 12 x 12
V = 2880
Therefore, the volume of the prism is 2880 cubic inches.
The above-given dimensions for the land carrier:
length = 19; width = 12; height = 10
The volume of the rectangular prism = length x width x height
V = 19 x 12 x 10
V = 2280
Therefore, the volume of the prism is 2280 cubic inches.
Therefore, the land carrier has a greater volume.
HOT Problems
Question 11.
Mathematical PRACTICE Use Number Sense Explain how the Associative Property can be used to mentally find the volume of the prism shown.
Answer:
V= l × w × h Volume formula
V= 20 x 18 x 5
V = 20 x ( 18 x 5 ) Associative Property
V = 20 × 90 Multiply.
V = 1800
The volume of the prism is 1800 cm3.
Question 12.
Building on the Essential Question How do I find the volume of rectangular prisms?
Answer:
The volume of a rectangular prism is the measurement of the total space inside it.
The formula for the volume of a rectangular prism = base area × height of the prism. Since the base of a rectangular prism is a rectangle, its area will be l × w. This area is then multiplied by the height of the prism to get the volume of the prism. Therefore, another way to express this formula is by multiplying the length, width, and height of the prism and writing the value in cubic units (cm3, m3, in3, etc).
Therefore, the volume of a rectangular prism = length x width x height.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 9 My Homework Answer Key
Practice
Find the volume of each prism.
Question 1.
V = ______________
Answer:
The above dimensions:
length = 10; width = 8; height = 15
The volume of the rectangular prism = length x width x height
V = 10 x 8 x 15
V = 1200
Therefore, the volume of the prism is 1200 cubic yards.
Question 2.
V = ______________
Answer:
The above dimensions:
base area = 176; height = 4
The volume of the rectangular prism = base area x height
– Since the base of a rectangular prism is a rectangle, its area will be l × w. This area is then multiplied by the height of the prism to get the volume of the prism.
V = 176 x 4
V = 704
Therefore, the volume of the prism is 704 cubic centimetres.
Vocabulary Check
Fill in the blank with the correct term or number to complete the sentence.
Question 3.
Volume is measured in ______________ units.
Answer: cubic
The volume of a rectangular prism is the measurement of the total space inside it.
The formula for the volume of a rectangular prism = base area × height of the prism. Since the base of a rectangular prism is a rectangle, its area will be l × w. This area is then multiplied by the height of the prism to get the volume of the prism. Therefore, another way to express this formula is by multiplying the length, width, and height of the prism and writing the value in cubic units (cm3, m3, in3, etc).
Therefore, the volume of a rectangular prism = length x width x height.
Problem Solving
Question 4.
The Donaldson’s swimming pool measures 15 meters long, 8 meters wide, and 3 meters deep. How many cubic meters of water will the pool hold?
Answer:
The length of the swimming pool = 15
The width of the swimming pool = 8
The height of the swimming pool = 3
We need to find out the volume of water a pool can hold. Let it be V.
The volume of the rectangular prism = length x width x height
V = 15 x 8 x 3
V = 360
Therefore, the volume of the swimming pool is 360 cubic metres
Question 5.
The hotel that the Hutching family is staying at on vacation is shaped like a rectangular prism, It is 234 feet long, 158 feet wide, and 37 feet tall. What is the volume of the hotel?
Answer:
The above-given:
length = 234; width = 158; height = 37
The volume of the rectangular prism = length x width x height
V = 234 x 158 x 37
V = 1367964
Therefore, the volume of the hotel is 1367964 cubic feet.
Question 6.
Jena keeps her recipes in a box with dimensions 7 inches, 5 inches, and 4 inches. What is the volume of the box?
Answer:
The above-given dimensions:
The length of the box = 7
The width of the box = 5
The height of the box = 4
The volume of the box = h
The volume of the rectangular prism = length x width x height
V = 7 x 5 x 4
V = 140
Therefore, the volume of the box is 140 cubic inches.
Question 7.
Mathematical PRACTICE Model Math Describe the dimensions of two different prisms that each have a volume of 2,400 cubic centimetres. Then draw each prism.
Answer:
The above-given:
Volume = 2400
The volume of the rectangular prism = length x width x height
You need three numbers that multiply to get that number.10, 10, and 24
The dimensions for another prism are 10, 20, and 12
If we calculate this:
V = l x w x h
2400 = 10 x 10 x 24
2400 = 2400
The other prism:
2400 = 10 x 20 x 12
2400 = 2400
Hence, the answer is proven.
Test Practice
Question 8.
What is the volume of the prism formed by the luggage bag?
(A) 6,000 in3
(B) 6,600 in3
(C) 7,200 in3
(D) 7,400 in3
Answer: Option B is the correct answer.
The above-given dimensions:
The length of the bag = 22
The width of the bag = 10
The height of the bag = 30
The volume of the box = h
The volume of the rectangular prism = length x width x height
V = 22 x 10 x 30
V = 6600
Therefore, the volume of the box is 6600 cubic inches.