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

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If the rectangular solid in the illustration above has the same volume  [#permalink]

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New post Updated on: 22 Aug 2018, 21:39
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A
B
C
D
E

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  25% (medium)

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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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Originally posted by s55day on 22 Aug 2018, 19:44.
Last edited by s55day on 22 Aug 2018, 21:39, edited 2 times in total.
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Re: If the rectangular solid in the illustration above has the same volume  [#permalink]

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New post 22 Aug 2018, 21:34
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If the rectangular solid in the illustration above has the same volume  [#permalink]

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New post 22 Aug 2018, 22:06
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   [#permalink] 22 Aug 2018, 22:06
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