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# If the rectangular solid in the illustration above has the same volume

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Intern
Joined: 17 Jul 2018
Posts: 37
Location: United States (CA)
Concentration: Strategy, Organizational Behavior
Schools: CBS
GMAT 1: 200 Q1 V1
GPA: 3
WE: Sales (Consulting)
If the rectangular solid in the illustration above has the same volume  [#permalink]

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Updated on: 22 Aug 2018, 20:39
00:00

Difficulty:

25% (medium)

Question Stats:

86% (02:08) correct 14% (02:47) wrong based on 7 sessions

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If the rectangular solid in the illustration below has the same volume as a cube with sides of length a, what is the surface area of the rectangular solid in terms of a?
A.2a^2
B.4a^2
C.7a^2
D.8a^2
E.10a^2

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Screen Shot 2018-08-22 at 10.45.28 PM.png [ 11.09 KiB | Viewed 268 times ]

Originally posted by s55day on 22 Aug 2018, 18:44.
Last edited by s55day on 22 Aug 2018, 20:39, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51214
Re: If the rectangular solid in the illustration above has the same volume  [#permalink]

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22 Aug 2018, 20:34
s55day wrote:
If the rectangular solid in the illustration above has the same volume as a cube with sides of length a, what is the surface area of the rectangular solid in terms of a?
A.2a^2
B.4a^2
C.7a^2
D.8a^2
E.10a^2

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Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
If the rectangular solid in the illustration above has the same volume  [#permalink]

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22 Aug 2018, 21:06
s55day wrote:
If the rectangular solid in the illustration below has the same volume as a cube with sides of length a, what is the surface area of the rectangular solid in terms of a?
A.2a^2
B.4a^2
C.7a^2
D.8a^2
E.10a^2

Given, Area of cuboid=Area of cube
Or, $$L*W*H=L^3$$
Or, $$a*2a*H=a^3$$
Or, $$H=\frac{a^3}{a*2a}$$
Or, $$H=\frac{a}{2}$$

Surface area of cuboid=$$2(LW+LH+HW)=2(a*2a+a*\frac{a}{2}+\frac{a}{2}*2a)=2*\frac{7a^2}{2}=7a^2$$

Ans. (C)
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If the rectangular solid in the illustration above has the same volume &nbs [#permalink] 22 Aug 2018, 21:06
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