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# What is the volume of a cube with surface area 54x^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 50570
What is the volume of a cube with surface area 54x^2?  [#permalink]

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04 Dec 2017, 21:55
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:18) correct 22% (01:25) wrong based on 26 sessions

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What is the volume of a cube with surface area 54x^2?

(A) 9x^2
(B) 27x^3
(C) 81x^2
(D) 81x^3
(E) 729x^3

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Joined: 24 Nov 2016
Posts: 152
Re: What is the volume of a cube with surface area 54x^2?  [#permalink]

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05 Dec 2017, 04:40
Bunuel wrote:
What is the volume of a cube with surface area 54x^2?

(A) 9x^2
(B) 27x^3
(C) 81x^2
(D) 81x^3
(E) 729x^3

Surface area of a cube: $$6*side^2 = 54x^2; side^2 = \frac{54x^2}{6}; side = \sqrt{9x^2}; side = 3x$$
Volume of a cube: $$side^3 = (3x)^3 = 27x^3$$

Re: What is the volume of a cube with surface area 54x^2? &nbs [#permalink] 05 Dec 2017, 04:40
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