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The areas of three faces of a rectangular solid are 12, 15 and 20. Wha
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16 Jun 2021, 04:28
16 Jun 2021, 04:28
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The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?
A. 30
B. 60
C. 180
D. 900
E. 3600
A. 30
B. 60
C. 180
D. 900
E. 3600
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Joined: 10 Apr 2015
Posts: 6218
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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha
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16 Jun 2021, 05:10
16 Jun 2021, 05:10
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Carcass wrote:
The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?
A. 30
B. 60
C. 180
D. 900
E. 3600
A. 30
B. 60
C. 180
D. 900
E. 3600
Let x = the width
Let y = the length
Let z = the height
So, the volume = xyz
Area of one face = 12
We can write: xy = 12
Area of one face = 15
We can write: xz = 15
Area of one face = 20
We can write: yz = 20
Combine to get: (xy)(xz)(yz) = (12)(15)(20)
Simplify: x²y²z² = 3600
Rewrite as: (xyz)² = 60²
So, xyz = 60
In other words, the volume = 60
Answer: B
Cheers,
Brent
Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha
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29 Jul 2023, 13:42
29 Jul 2023, 13:42
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