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The areas of faces A, B, and C of the rectangular solid shown in the a

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The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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New post 04 Jan 2018, 00:31
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A
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E

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[GMAT math practice question]

Attachment:
20180104_173047.png
20180104_173047.png [ 1.22 KiB | Viewed 520 times ]


The areas of faces A, B, and C of the rectangular solid shown in the above figure are 12, 15, and 20, respectively. What is the volume of the solid?

A. 36
B. 48
C. 60
D. 64
E. 72

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Re: The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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New post 04 Jan 2018, 00:41
MathRevolution wrote:
[GMAT math practice question]

Attachment:
20180104_173047.png


The areas of faces A, B, and C of the rectangular solid shown in the above figure are 12, 15, and 20, respectively. What is the volume of the solid?

A. 36
B. 48
C. 60
D. 64
E. 72


As it is rectangular solid areas of faces A, B, and C = l*b,b*h,l*h

Volume of the solid is l*b*h

So l*b*b*h*l*h = \(l^2*b^2*h^2\)

Volume of the solid =\sqrt{\(l^2*b^2*h^2\)}

=\sqrt{12*15*20}=60
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Director
Director
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Posts: 525
Location: India
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GPA: 3.35
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Re: The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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New post 04 Jan 2018, 00:42
MathRevolution wrote:
[GMAT math practice question]

Attachment:
20180104_173047.png


The areas of faces A, B, and C of the rectangular solid shown in the above figure are 12, 15, and 20, respectively. What is the volume of the solid?

A. 36
B. 48
C. 60
D. 64
E. 72


As it is rectangular solid areas of faces A, B, and C = l*b,b*h,l*h

Volume of the solid is l*b*h

So l*b*b*h*l*h = \(l^2*b^2*h^2\)

Volume of the solid =\sqrt{\(l^2*b^2*h^2\)}

=\sqrt{12*15*20}=60

Hence C
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6613
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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New post 07 Jan 2018, 17:16
=>

Let \(a\) and \(b\) be the edges of face \(A\), and let \(b\) and \(c\) be the edges of face \(B\). Then the edges of face \(C\) are \(a\) and \(c\). Moreover, the volume of the solid is \(abc\). Now,
\(ab = 12\), \(bc = 15\) and \(ca = 20\).
Multiplying these together yields
\((ab)(bc)(ca) = a^2b^2c^2 = (abc)^2 = 12*15*20 = 3600 = 60^2\)
So \(abc = 60\).
Therefore, the answer is C.

Answer: C
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Re: The areas of faces A, B, and C of the rectangular solid shown in the a &nbs [#permalink] 07 Jan 2018, 17:16
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