NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
6•5
Lesson 14: Volume in the Real World
Classwork
Example 1
a.
The area of the base of a sandbox is 9
1 2
1
ft . The volume of the sandbox is 7 ft 3 . Determine the height of the
2
8
sandbox.
b.
The sandbox was filled with sand, but after kids played, some of the sand spilled out. Now, the sand is at a
height of
1
ft. Determine the volume of the sand.
2
Lesson 14:
Date:
Volume in the Real World
2/8/16
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Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
6•5
Example 2
A special order sandbox has been created for children to use as an archeological digging area at the zoo. Determine the
volume of the sandbox.
𝟓𝐦
𝟐𝐦
𝟏
𝐦
𝟓
𝟐
𝟏
𝐦
𝟑
𝟑
𝟐 𝐦
𝟒
𝟒
𝟏
𝐦
𝟑
𝟏
𝟐 𝐦
𝟒
Exercises
1.
a.
The volume of the rectangular prism is given. Determine the missing measurement using a one-step equation.
𝑽=
𝟑𝟔
𝐲𝐝𝟑
𝟏𝟓
𝐀𝐫𝐞𝐚 =
𝟒
𝐲𝐝𝟐
𝟓
𝒉=?
Lesson 14:
Date:
Volume in the Real World
2/8/16
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Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
b.
The volume of the box is
6•5
45 3
m . Determine the area of the base using a one-step equation.
6
𝟗
𝐦
𝟐
2.
Marissa’s fish tank needs to be filled with more water.
a.
Determine how much water the tank can hold.
𝟑
𝐦
𝟓
𝟑
𝐦
𝟖
𝟑
𝐦
𝟒
b.
Determine how much water is already in the tank.
c.
How much more water is needed to fill the tank?
Lesson 14:
Date:
𝟏
𝐦
𝟒
Volume in the Real World
2/8/16
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
3.
6•5
Determine the volume of the composite figures.
a.
𝟑
𝟏𝟐 𝐦
𝟐
𝟗
𝟏
𝐦
𝟐
𝟏
𝐦
𝟒
𝟏
𝐦
𝟑
𝟐𝐦
b.
𝟏
𝟏
𝐟𝐭.
𝟐
𝟏
𝐟𝐭.
𝟐
𝟏
𝐟𝐭.
𝟐
𝟑
𝐟𝐭.
𝟒
𝟏
𝐟𝐭.
𝟒
𝟏
Lesson 14:
Date:
𝟏
𝐟𝐭.
𝟐
Volume in the Real World
2/8/16
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
6•5
Problem Set
1.
The volume of a rectangular prism is
21 3
3
ft , and the height of the prism is ft. Determine the area of the base.
12
4
2.
The volume of a rectangular prism is
10 3
2
ft . The area of the base is ft 2 . Determine the height of the rectangular
21
3
prism.
3.
Determine the volume of the space in the tank that still needs to be filled with water if the water is
1
ft. deep.
3
𝟐 𝐟𝐭.
𝟏
𝟐
𝐟𝐭.
𝟑
𝟓 𝐟𝐭.
4.
Determine the volume of the composite figure.
𝟑
𝐦
𝟒
𝟏
𝐦
𝟖
𝟏
𝐦
𝟑
𝟏
𝐦
𝟑
𝟏
𝐦
𝟒
5.
Determine the volume of the composite figure.
𝟏 𝐢𝐧.
𝟏
𝟏
𝐢𝐧.
𝟐
𝟏
𝐢𝐧.
𝟒
𝟏
𝟏 𝐢𝐧.
𝟒
𝟐
𝟏
𝐢𝐧.
𝟐
𝟑 𝐢𝐧.
Lesson 14:
Date:
Volume in the Real World
2/8/16
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
6•5
6.
𝟏𝐦
𝟑
𝟏
𝐦
𝟐
𝟏
𝟏
𝐦
𝟒
𝟐𝐦
𝟕
𝟏
𝐦
𝟒
a.
Write an equation to represent the volume of the composite figure.
b.
Use your equation to calculate the volume of the composite figure.
Lesson 14:
Date:
Volume in the Real World
2/8/16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.76
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.