McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures

All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 12 Lesson 11 Volume of Composite Figures will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 12 Lesson 11 Volume of Composite Figures

A composite figure is made up of two or more three-dimensional figures. To find the volume, separate the figure into figures with volumes you know how to find.

Math in My World

Example 1

The Arc de Triomphe in Paris. France, is roughly ¡n the shape of the composite figure shown. Find the volume of the Arc de Triomphe.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 1
Separate the figure into three rectangular prisms. Find the volume of each prism.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 2
So, the total volume is ___________ cubic yards, or _____________ yd3.
Answer:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_1
Therefore, the total volume is 52,512 cubic yards or 52,512 yd^3.

Example 2

Find the volume of the composite figure.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 3
Separate the figure into two prisms. Find the volume of each prism.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 4
Add the volumes. The total volume is _______________ cubic meters, or _____________ m3.
Answer:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_2
add the volume: 0.88 + 0.8 = 1.68
The total volume is 1.68 cubic metres or 1.68 m^3.

Guided Practice

Question 1.
Find the volume of the composite figure.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 5
Bottom Prism
V = B Ă— h
V = 126 Ă— 11
V = ____________

Top Prism
V = l Ă— w Ă— h
V = 2 Ă— 9 Ă— 5
V = 2 Ă— (9 Ă— 5) Associative Property
V = 2 Ă— 45
V = ______________
The total volume is ____________ + _____________ or ______________ cubic centimeters.
Answer:
Bottom prism:
Let us consider a square prism with a square base.
V = Area of base Ă— Height of the prism
V = B x h
V = 126 x 11
V = 1386 cubic centimetre
Therefore, the bottom prism volume is 1386 cm^3.
Top Prism
The volume of the rectangular prism, V = l x w x h
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 2 Ă— 9 Ă— 5
V = 2 Ă— (9 Ă— 5) Associative Property
V = 2 Ă— 45
V = 90
Now add both the prism to get the total volume:
The total volume is 1386 + 90 = 1476
Therefore, the total volume is 1476 cubic centimetres.

Independent Practice

Find the volume of each composite figure.

Question 2.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 6
V = _______________
Answer:
Bottom prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 8 Ă— 6 Ă— 5
V = 240
Top prism:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_3
V = l Ă— w Ă— h
V = 5 Ă— 6 Ă— 3
V = 90
Now add both the prisms to get the total volume:
V(add) = bottom prism + top prism
V(add) = 240 + 90|
V(add) = 330
Therefore, the total volume is 330 cubic metres.

Question 3.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 7
V = _______________
Answer:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_4
We split the figure into three prisms:
1. Top prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 12 x 4 x 2
V = 96
2. Bottom prism:
V = l Ă— w Ă— h
V = 2 x 3 x 4
V = 24
3. bottom prism:
V = l Ă— w Ă— h
V = 2 x 3 x 4
V = 24
Now add all the prism values:
V(add) = 96 + 24 + 24
V(add) = 144
Therefore, the total volume of the figure is 144 cubic centimetres.

Question 4.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 8
V = _______________
Answer:
Bottom prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 9 Ă— 5 Ă— 4
V = 180
Top prism:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_5
V = l Ă— w Ă— h
V = 5 Ă— 5 Ă— 4
V = 100
Now add both the prisms to get the total volume:
V(add) = bottom prism + top prism
V(add) = 180 + 100
V(add) = 280
Therefore, the total volume is 280 cubic yards.

Question 5.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 9
V = _______________
Answer:
1. Top prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 7 x 3 x 1.5
V = 31.5
2. Bottom prism:
V = l Ă— w Ă— h
V = 11 x 6 x 4
V = 264
Now add both the prisms to get the total volume of the figure:
V(add) = 31.5 + 264
V(add) = 295.5
Therefore, the total volume of the figure is 295.5 cubic feet.

Question 6.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 10
V = _______________
Answer:
Bottom prism:
Let us consider a square prism with a square base.
V = Area of base Ă— Height of the prism
V = B x h
V = 384 x 5
V = 1920 cubic yards
Therefore, the bottom prism volume is 1920 cubic yards.
Top Prism
The volume of the rectangular prism, V = l x w x h
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 11 Ă— 9 Ă— 4
V = 396
Now add both the prism to get the total volume:
The total volume is 1920 + 396 = 2316
Therefore, the total volume is 2316 cubic yards.

Independent

Question 7.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 11
V = _______________
Answer:
Bottom prism:
Let us consider a square prism with a square base.
V = Area of base Ă— Height of the prism
V = B x h
V = 21 x 2
V = 42
Therefore, the bottom prism volume is 42 cubic mm
Top Prism
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_6
The volume of the rectangular prism, V = l x w x h
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 3 Ă— 3 Ă— 2
V = 18
Now add both the prism to get the total volume:
The total volume is 42 + 18 = 60
Therefore, the total volume is 60 cubic mm.

Problem Solving

Question 8.
Mrs. Stafford ordered the set of blocks shown at the right for her classroom. Find the total volume of all the blocks.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 12
Would all of the blocks fit in a shipping box with a length of 4 inches, a width of 4 inches, and a height of 4 inches? Explain.
Answer:
The volumes are given directly.
Add all the volumes:
V(add) = 8 + 12 + 8 + 16 + 8 + 16
V(add) = 68
Therefore, the total volume of all the blocks is 68 cubic inches.
The sample answer is given:
No, the volume of the shipping box is less than the volume of the blocks so they will not fit.

Question 9.
The figure represents a piece of foam packaging. Find the volume of the foam.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 13
Answer:
The volume of the rectangular prism, V = l x w x h
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 7 Ă— 2 Ă— 1
V = 14
Another prism:
V = l Ă— w Ă— h
V = 7 Ă— 3 Ă— 1
V = 21
Now add both the prism to get the total volume:
The total volume is 14 + 21 = 35
Therefore, the total volume of the foam is 35 cubic feet.

HOT Problems

Question 10.
Mathematical PRACTICE Which One Doesn’t Belong? Circle the figure that is not a composite figure.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 14
Answer:
A composite figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures.
The middle figure cannot split so this is not a composite figure.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_7

Question 11.
Building on the Essential Question How can I find the volume of a composite figure?
Answer:
Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:
Step 1: Break down the compound shape into different components.
Step 2: Determine the volume of each basic shape.
Step 3: Combine the volumes of all the basic shapes.
Step 4: Write the solution in cubic units.

McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 My Homework Answer Key

Practice

Find the volume of each composite figure.

Question 1.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 15
V = ______________
Answer:
1. Top prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 5 x 3 x 1
V = 15
2. Bottom prism:
V = l Ă— w Ă— h
V = 7 x 3 x 3
V = 63
Now add both the prisms to get the total volume of the figure:
V(add) = 15 + 63
V(add) = 78
Therefore, the total volume of the figure is 78 cubic feet.

Question 2.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 16
V = ______________
Answer:
Let us consider a square prism with a square base.
V = Area of base Ă— Height of the prism
V = B x h
V = 6 x 5.5
V = 33 cubic metres
Therefore, the bottom prism volume is 33 cubic metres
Top Prism
The volume of the rectangular prism, V = l x w x h
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 5.5 Ă— 1 Ă— 1
V = 5.5
Now add both the prism to get the total volume:
The total volume is 33 + 5.5 = 38.5
Therefore, the total volume is 38.5 cubic metres

Problem Solving

Question 3.
Maci is decorating the cake shown. Find the volume of the cake.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 17
Answer:
1. Top prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 9 x 9 x 4
V = 324 cubic inches
2. Bottom prism:
V = l Ă— w Ă— h
V = 12 x 12 x 3
V = 432 cubic inches
Now add both the prisms to get the total volume of the figure:
V(add) = 324 + 432
V(add) = 756
Therefore, the total volume of the figure is 756 cubic inches.

Question 4.
The firehouse shown is in the shape of a composite figure. How many cubic yards of space are in the firehouse?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 18
Answer:
1. Top prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 40 x 15 x 12
V = 7200
2. Bottom prism:
V = l Ă— w Ă— h
V = 20 x 15 x 7
V = 2100
Now add both the prisms to get the total volume of the figure:
V(add) = 7200 + 2100
V(add) = 9300
Therefore, the total volume of the figure is 9300 cubic yards.

Question 5.
Mathematical PRACTICE Model Math Draw an example of a composite figure that has a volume between 750 and 900 cubic units.
Answer:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_9
Bottom prism:
The volume of the rectangular prism:
V = l x w x h
V = 6 x 5 x 3
V = 90 cubic feet
Therefore, the bottom prism volume is 90 cubic feet
Top Prism
The volume of the rectangular prism, V = l x w x h
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 12 x 10 x 6
V = 720
Now add both the prism to get the total volume:
The total volume is 90 + 720 = 810
Therefore, the total volume is 810 cubic feet.
810 is between 750 and 900 cubic units.

Vocabulary Check

Fill in the blank with the correct term or number to complete the sentence.

Question 6.
A ____________ is made up of two or more three-dimensional figures.
Answer: composite figure.
Two or more solid figures are combined to create a composite figure. You can determine the volume of a composite figure by dismantling it.
Example:
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures_8

Test Practice

Question 7.
What is the total volume of the composite figure?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 11 Answer Key Volume of Composite Figures 19
(A) 282 cubic centimetres
(B) 432 cubic centimetres
(C) 492 cubic centimetres
(D) 502 cubic centimetres
Answer: Option C is the correct answer.
1. Top prism:
The volume of the rectangular prism = l x w x h
“l” is the base length
– “w” is the base width
– “h” is the height of the prism
V = l Ă— w Ă— h
V = 5 x 3 x 4
V = 60
2. Bottom prism:
V = l Ă— w Ă— h
V = 9 x 6 x 8
V = 432
Now add both the prisms to get the total volume of the figure:
V(add) = 60 + 432
V(add) = 492
Therefore, the total volume of the figure is 492 cubic centimetres

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