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# Q is a cube. Find the volume of the cube.

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Math Expert
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Q is a cube. Find the volume of the cube.  [#permalink]

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24 Feb 2015, 08:00
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5% (low)

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92% (00:36) correct 8% (01:06) wrong based on 259 sessions

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Q is a cube. Find the volume of the cube.

(1) The total surface area of Q is 150 sq cm
(2) The distance from one vertex of Q to the catty-corner opposite vertex is 5*sqrt(3)

Kudos for a correct solution.

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Re: Q is a cube. Find the volume of the cube.  [#permalink]

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24 Feb 2015, 08:18
Let x be side of the cube.
1) The total surface area of cube = 6*x^2 =we can use this get x and the volume
2) diagonal connecting opposite corner =x*sqrt(3) =(sqrt(x^2+(xsqrt(2))^2))= 5 sqrt(3) we can use this get x and the volume

answer>> D
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Re: Q is a cube. Find the volume of the cube.  [#permalink]

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24 Feb 2015, 08:25
1
The correct answer is D. If we have one side of a cube, we can find the volume: $$V = s^3$$

(1) SA of one side of the cube is $$150/6 = 25$$
SA of one side of a cube is $$s^2$$ so $$s^2 = 25$$ and $$s = 5$$ [Sufficient]

(2) Diagonal of a cube is $$\sqrt{3(s^2)}$$ = $$5\sqrt{3}$$
$$(5\sqrt{3})^2$$ = $$25*3$$ = $$75$$ so $$3s^2 = 75$$
$$s^2 = 25$$ and $$s = 5$$ [Sufficient]
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Re: Q is a cube. Find the volume of the cube.  [#permalink]

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02 Mar 2015, 07:19
Bunuel wrote:
Q is a cube. Find the volume of the cube.

(1) The total surface area of Q is 150 sq cm
(2) The distance from one vertex of Q to the catty-corner opposite vertex is 5*sqrt(3)

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Another simple prompt, and again, we need the volume.

Statement #1 tells us surface area is 150. Well, for a cube, SA = 6s^2. If we know 150 = 6s^2, we can solve for s, which will allow us to calculate the volume. Statement #1 is by itself sufficient.

Statement #2 tell us the space diagonal has a length of $$5*\sqrt{3}$$. Well, the three-dimensional version of the Pythagorean Theorem tell us that:

$$(5*\sqrt{3})^2 = s^2 + s^2 + s^2$$

That would allow us to solve for s, which would allow us to calculate the volume. Statement #2 is by itself sufficient.

Both statements sufficient by themselves. Answer = D.
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Posts: 55225
Re: Q is a cube. Find the volume of the cube.  [#permalink]

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02 Mar 2015, 07:29
Bunuel wrote:
Q is a cube. Find the volume of the cube.

(1) The total surface area of Q is 150 sq cm
(2) The distance from one vertex of Q to the catty-corner opposite vertex is 5*sqrt(3)

Kudos for a correct solution.

Check other 3-D Geometry Questions in our Special Questions Directory.
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Re: Q is a cube. Find the volume of the cube.  [#permalink]

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05 May 2015, 20:08
It was an easy one.
Given: Q is a cube , so all sides are equal.
A) We know the surface area so length of a side can be calculated. SO A is sufficient. A or D can be the only answer . rule out B,C ,and E.
B) We know the diagonal length so again we can calculate the side length and gets volume of the cube. SO B is also sufficient.

A and B alone are sufficient. D is the answer
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Q is a cube. Find the volume of the cube.  [#permalink]

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26 May 2016, 14:59
Given that Q is a cube we have find its volume

Statement 1 gives information about the total surface area of the cube = 150 sq.cm
we know that cube has 6 equal faces area of single face = 25 which in turn gives us the side as 5 cm
Volume of cube = 125 cu.cm
So sufficient

Statement 2 gives the length of longest diagonal of the cube as 5 *$$\sqrt{3}$$
this in turn gives us the side as 5 cm
Volume of cube = 125 cu.cm
So sufficient

Correct Answer - D
Q is a cube. Find the volume of the cube.   [#permalink] 26 May 2016, 14:59
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# Q is a cube. Find the volume of the cube.

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