Volume of Rectangular Prisms
Name
12.3
?
Geometry and Measurement—5.6.B Also 5.4.G MATHEMATICAL PROCESSES 5.1.F, 5.1.G
Volume of Rectangular Prisms
Essential Question
How can you find the volume of a rectangular prism?
Connect The base of a rectangular prism is a rectangle. You know that area is measured in square units and that the area of a rectangle can be found by multiplying the length and the width. Volume is measured in cubic units, such as cubic feet or cu ft. When you build a prism and add each layer of cubes, you are adding a third dimension, height.
The area of the base is _ sq units.
Unlock Unlock the the Problem Problem Sid built the rectangular prism shown at the right, using 1-inch cubes. The prism has a base that is a rectangle and has a height of 4 cubes. What is the volume of the rectangular prism that Sid built?
112 112
You can find the volume of a prism in cubic units by multiplying the number of square units in the base shape by the number of layers, or its height.
112
Each layer of Sid’s rectangular prism 12
is composed of _ inch cubes. Height (in layers)
1
2
Volume (in cubic inches)
12
24
3
4
Multiply the height by _.
1. How does the volume change as each layer is added?
© Houghton Mifflin Harcourt Publishing Company
2. What does the number you multiply the height by represent?
So, the volume of Sid’s rectangular prism is _ cu in.
Module 12
447
Share Share and and Show Show Find the volume. 1. The length of the rectangular prism is __.
5 cm
The width is __. So, the area of the base is __.
4 cm
The height is __. So, the volume of the prism is __. 2.
2 cm
3.
3 ft 3 ft 4 ft Volume: __
2 in.
5 in. 2 in.
Volume: __
Math Talk Mathematical Processes
Problem Problem Solving Solving 4. Explain what else you need to know to find the volume of a rectangular
How many more layers should be added to the prism in Exercise 3 so that the volume of the prism is 60 cubic inches? Explain.
5.
Reasoning How can you find the volume of a cube if you know the area of the base is 25 sq cm?
6.
The volume of a rectangular prism is 40 cu ft. The height of the prism is 10 ft. What is the area of the base of the prism? Explain.
448
© Houghton Mifflin Harcourt Publishing Company
prism if you know the area of the base.
Name
Problem Problem Solving Solving 7. Kayan is designing a box for sugar cubes. Each sugar cube has a volume
of 1 cubic inch. Kayan wants to have 12 cubes in each layer. If he wants to fit 60 cubes in each box, how tall should the box be?
8.
Multi-Step Golf balls are packed in cardboard boxes that are 2 inches long, 2 inches wide, and 2 inches high. The boxes are then packed into larger containers that are 20 inches long, 30 inches wide, and 20 inches high. How many golf balls can fit in the larger container?
2 in. 20 in.
30 in. 20 in.
9. Multi-Step Yvette uses centimeter cubes to make a bed for her doll.
The bed is in the shape of a rectangular prism. She wants the length of the prism to be 15 cm. The width should be 5 cm and the height 5 cm. How many centimeter cubes does Yvette need?
© Houghton Mifflin Harcourt Publishing Company
10.
Multi-Step Cameron uses a rectangular baking pan with a base measuring 12 square inches. Cameron pours batter in the pan so that it is 2 inches deep. The finished cake will be 3 times as tall as the batter. What is the volume of the cake?
Module 12 • Lesson 3
449
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. 11. A cube-shaped block of cheese has side lengths of 6 inches. The block
of cheese is cut into smaller pieces. Each piece has a volume of 1 cubic inch. How many pieces of cheese will there be?
A
18 pieces
B
36 pieces
C
216 pieces
D
72 pieces
12. Frank is packing cube-shaped containers into large boxes. He can fit
15 containers in each layer. If he stacks 8 layers into one box, what is the volume of the box?
A
64 cubes
C
128 cubes
B
120 cubes
D
256 cubes
13. Multi-Step A rectangular block of cheese has a length of 8 centimeters,
a width of 4 centimeters, and a height of 3 centimeters. If the block is cut into two equal pieces, what will be the volume of each piece?
A
15 cubic cm
B
28 cubic cm
C
48 cubic cm
D
96 cubic cm
TEXAS Test Prep A
28 sq cm
B
140 sq cm
C
28 cu cm
D
450
140 cu cm
5 cm 4 cm 7 cm
© Houghton Mifflin Harcourt Publishing Company
14. What is the volume of the rectangular prism at the right?
Geometry and Measurement—5.6.B Also 5.4.G MATHEMATICAL PROCESSES 5.1.F, 5.1.G
H o mewo rk and Practice
12.3
Name
Volume of Rectangular Prisms
Find the volume. 1.
2.
2 ft
3 cm
3 ft
2 cm
8 ft
5 cm Volume: __
Volume: __
3.
4.
5 cm
6 in.
3 cm 2 in.
2 in.
3 cm
Volume: __
5.
Volume: __
6.
4 in.
4 ft
3 ft 5 in. 3 in.
2 ft Volume: __
Volume: __
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
7. Vijay has a collection of 50 number cubes that
are each 1 cubic inch. He finds a box that is 4 inches high. He fits 12 cubes into the bottom of the box. Can Vijay fit all his number cubes into the box? Explain.
8. Maya wants to use 1-centimeter cubes to
make a larger cube with side lengths of 3 centimeters. How many 1-centimeter cubes will Maya need?
Module 12 • Lesson 3 451
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer. shown below?
5 in.
2 in. 6 in.
A
12 sq in.
B
60 sq in.
C
12 cu in.
D
60 cu in.
11. Jaden fills a box with 32 cubes. The box is
4 cubes long and 2 cubes wide. How many layers of cubes are in the box?
A
3
B
4
C
8
D
5
13. Multi-Step The shipping clerk packs a cube
with side lengths of 8 inches into a box with side lengths of 10 inches. What is the volume of the space left in the larger box for packing materials?
452
A
598 cubic inches
B
1,000 cubic inches
C
512 cubic inches
D
488 cubic inches
10. Miranda packs cube-shaped jewelry boxes
into a display box that is a rectangular prism. In the bottom layer, she can fit 4 rows of 7 jewelry boxes. If she stacks 6 layers into the display box, what is the volume of the display box?
A
168 cubes
B
28 cubes
C
196 cubes
D
66 cubes
12. Javier has forty 1-centimeter cubes. He builds
a rectangular prism with 6 cubes in the bottom layer. He wants to have the fewest cubes left over. How many layers can Javier make?
A
7
B
5
C
6
D
8
14. Multi-Step The volume of cube A is 64 cubic
feet. What is the volume of cube B if its side lengths are half the length of cube A’s sides?
A
8 cubic feet
B
32 cubic feet
C
16 cubic feet
D
4 cubic feet
© Houghton Mifflin Harcourt Publishing Company
9. What is the volume of the rectangular prism
12.3
?
Geometry and Measurement—5.6.B Also 5.4.G MATHEMATICAL PROCESSES 5.1.F, 5.1.G
Volume of Rectangular Prisms
Essential Question
How can you find the volume of a rectangular prism?
Connect The base of a rectangular prism is a rectangle. You know that area is measured in square units and that the area of a rectangle can be found by multiplying the length and the width. Volume is measured in cubic units, such as cubic feet or cu ft. When you build a prism and add each layer of cubes, you are adding a third dimension, height.
The area of the base is _ sq units.
Unlock Unlock the the Problem Problem Sid built the rectangular prism shown at the right, using 1-inch cubes. The prism has a base that is a rectangle and has a height of 4 cubes. What is the volume of the rectangular prism that Sid built?
112 112
You can find the volume of a prism in cubic units by multiplying the number of square units in the base shape by the number of layers, or its height.
112
Each layer of Sid’s rectangular prism 12
is composed of _ inch cubes. Height (in layers)
1
2
Volume (in cubic inches)
12
24
3
4
Multiply the height by _.
1. How does the volume change as each layer is added?
© Houghton Mifflin Harcourt Publishing Company
2. What does the number you multiply the height by represent?
So, the volume of Sid’s rectangular prism is _ cu in.
Module 12
447
Share Share and and Show Show Find the volume. 1. The length of the rectangular prism is __.
5 cm
The width is __. So, the area of the base is __.
4 cm
The height is __. So, the volume of the prism is __. 2.
2 cm
3.
3 ft 3 ft 4 ft Volume: __
2 in.
5 in. 2 in.
Volume: __
Math Talk Mathematical Processes
Problem Problem Solving Solving 4. Explain what else you need to know to find the volume of a rectangular
How many more layers should be added to the prism in Exercise 3 so that the volume of the prism is 60 cubic inches? Explain.
5.
Reasoning How can you find the volume of a cube if you know the area of the base is 25 sq cm?
6.
The volume of a rectangular prism is 40 cu ft. The height of the prism is 10 ft. What is the area of the base of the prism? Explain.
448
© Houghton Mifflin Harcourt Publishing Company
prism if you know the area of the base.
Name
Problem Problem Solving Solving 7. Kayan is designing a box for sugar cubes. Each sugar cube has a volume
of 1 cubic inch. Kayan wants to have 12 cubes in each layer. If he wants to fit 60 cubes in each box, how tall should the box be?
8.
Multi-Step Golf balls are packed in cardboard boxes that are 2 inches long, 2 inches wide, and 2 inches high. The boxes are then packed into larger containers that are 20 inches long, 30 inches wide, and 20 inches high. How many golf balls can fit in the larger container?
2 in. 20 in.
30 in. 20 in.
9. Multi-Step Yvette uses centimeter cubes to make a bed for her doll.
The bed is in the shape of a rectangular prism. She wants the length of the prism to be 15 cm. The width should be 5 cm and the height 5 cm. How many centimeter cubes does Yvette need?
© Houghton Mifflin Harcourt Publishing Company
10.
Multi-Step Cameron uses a rectangular baking pan with a base measuring 12 square inches. Cameron pours batter in the pan so that it is 2 inches deep. The finished cake will be 3 times as tall as the batter. What is the volume of the cake?
Module 12 • Lesson 3
449
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. 11. A cube-shaped block of cheese has side lengths of 6 inches. The block
of cheese is cut into smaller pieces. Each piece has a volume of 1 cubic inch. How many pieces of cheese will there be?
A
18 pieces
B
36 pieces
C
216 pieces
D
72 pieces
12. Frank is packing cube-shaped containers into large boxes. He can fit
15 containers in each layer. If he stacks 8 layers into one box, what is the volume of the box?
A
64 cubes
C
128 cubes
B
120 cubes
D
256 cubes
13. Multi-Step A rectangular block of cheese has a length of 8 centimeters,
a width of 4 centimeters, and a height of 3 centimeters. If the block is cut into two equal pieces, what will be the volume of each piece?
A
15 cubic cm
B
28 cubic cm
C
48 cubic cm
D
96 cubic cm
TEXAS Test Prep A
28 sq cm
B
140 sq cm
C
28 cu cm
D
450
140 cu cm
5 cm 4 cm 7 cm
© Houghton Mifflin Harcourt Publishing Company
14. What is the volume of the rectangular prism at the right?
Geometry and Measurement—5.6.B Also 5.4.G MATHEMATICAL PROCESSES 5.1.F, 5.1.G
H o mewo rk and Practice
12.3
Name
Volume of Rectangular Prisms
Find the volume. 1.
2.
2 ft
3 cm
3 ft
2 cm
8 ft
5 cm Volume: __
Volume: __
3.
4.
5 cm
6 in.
3 cm 2 in.
2 in.
3 cm
Volume: __
5.
Volume: __
6.
4 in.
4 ft
3 ft 5 in. 3 in.
2 ft Volume: __
Volume: __
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
7. Vijay has a collection of 50 number cubes that
are each 1 cubic inch. He finds a box that is 4 inches high. He fits 12 cubes into the bottom of the box. Can Vijay fit all his number cubes into the box? Explain.
8. Maya wants to use 1-centimeter cubes to
make a larger cube with side lengths of 3 centimeters. How many 1-centimeter cubes will Maya need?
Module 12 • Lesson 3 451
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer. shown below?
5 in.
2 in. 6 in.
A
12 sq in.
B
60 sq in.
C
12 cu in.
D
60 cu in.
11. Jaden fills a box with 32 cubes. The box is
4 cubes long and 2 cubes wide. How many layers of cubes are in the box?
A
3
B
4
C
8
D
5
13. Multi-Step The shipping clerk packs a cube
with side lengths of 8 inches into a box with side lengths of 10 inches. What is the volume of the space left in the larger box for packing materials?
452
A
598 cubic inches
B
1,000 cubic inches
C
512 cubic inches
D
488 cubic inches
10. Miranda packs cube-shaped jewelry boxes
into a display box that is a rectangular prism. In the bottom layer, she can fit 4 rows of 7 jewelry boxes. If she stacks 6 layers into the display box, what is the volume of the display box?
A
168 cubes
B
28 cubes
C
196 cubes
D
66 cubes
12. Javier has forty 1-centimeter cubes. He builds
a rectangular prism with 6 cubes in the bottom layer. He wants to have the fewest cubes left over. How many layers can Javier make?
A
7
B
5
C
6
D
8
14. Multi-Step The volume of cube A is 64 cubic
feet. What is the volume of cube B if its side lengths are half the length of cube A’s sides?
A
8 cubic feet
B
32 cubic feet
C
16 cubic feet
D
4 cubic feet
© Houghton Mifflin Harcourt Publishing Company
9. What is the volume of the rectangular prism
