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What is the volume of Cube A?

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What is the volume of Cube A?  [#permalink]

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New post 24 Jan 2019, 04:53
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (00:48) correct 20% (01:07) wrong based on 90 sessions

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Re: What is the volume of Cube A?  [#permalink]

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New post 04 Jul 2019, 06:09
Bunuel wrote:
What is the volume of Cube A?

(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) m^2
(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\)


OFFICIAL EXPLANATION:



What is the volume of Cube A?

To solve this question you don't need to calculate anything or know any formula. Remember that in data sufficiency questions it's enough to know that you can solve for the value, and it's not always necessary to actually solve and get that value.

(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) \(m^2\). Knowing the surface area of a sphere, we can get the diameter of the sphere, which would be equal to the length of a side of the cube, and thus get the volume of the cube. Sufficient.

(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\). Basically the same here: the diameter of circumscribing sphere, will be equal to the length of a side of the cube, and thus we can get the volume of the cube. Sufficient.


Answer: D
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Re: What is the volume of Cube A?  [#permalink]

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New post 24 Jan 2019, 05:52
Bunuel wrote:
What is the volume of Cube A?

(1) The surface area of a sphere inscribed in Cube A is \(100\pi\) m^3
(2) The diameter of a sphere circumscribing Cube A is \(10\sqrt{3}\)


#1
surface area of sphere = 4* pi * r^2
4* pi * r^2 = 100 pi
r = 5 ; d = 10 sqrt3
side of cube can be determined ; sufficient
digonal of cube = s sqrt3

#2
given diameter = 10 sqrt 3
radius 5 sqrt 3
sufficeint

IMO D
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Re: What is the volume of Cube A?   [#permalink] 24 Jan 2019, 05:52
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