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What is the volume of the cube above?

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What is the volume of the cube above?  [#permalink]

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New post 26 Oct 2010, 09:07
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What is the volume of the cube above?

(1) The surface area of the cube is 600 square inches
(2) The length of diagonal AB is \(10\sqrt{3}\) inches

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Re: Volume of Cube  [#permalink]

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New post 26 Oct 2010, 09:28
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What is the volume of the cube above?

Let the side of the cube be \(x\), then the volume will be \(volume=x^3\)

(1) The surface area of the cube is 600 square inches --> surface area of a cube equals to {area of a face} * {# of faces} --> \(surface \ area=x^2*6=600\), --> \(x=10\)--> \(volume=x^3=1,000\). Sufficient.

(2) The length of diagonal AB is \(10\sqrt{3}\) inches --> diagonal of a cube equals to \(Diagonal=\sqrt{x^2+x^2+x^2}=x\sqrt{3}=10\sqrt{3}\) (x^2+x^2=square of a diagonal of a face and square of a diagonal of a face plus square of a side equals to diagonal of a cube) --> \(x=10\)--> \(volume=x^3=1,000\). Sufficient.

Answer: D.
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Re: Volume of Cube  [#permalink]

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New post Updated on: 26 Oct 2010, 09:37
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For volume of a cube ,we need to know the side of the cube as Volume of the cube is l^3 where l is side of the cube.

From (1)surface area is given means 6l^2 is given which is sufficient to get the value of l^3
From(2) length of diagonal l*sqrt(3) is given which is sufficient to get the value of l^3

Hence answer is D.

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Originally posted by ankitranjan on 26 Oct 2010, 09:19.
Last edited by ankitranjan on 26 Oct 2010, 09:37, edited 2 times in total.
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Re: What is the volume of the cube above?  [#permalink]

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Re: What is the volume of the cube above?  [#permalink]

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New post 21 Jun 2013, 00:17
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A cube is defined by only one value which is the length of its side. The internal angles always remain 90. So once you have the side, all other parameters of the cube inluding surface areas, volume, diagonals etc can be derived or alternatively once you have any of the other parameters the side can be derived. Straight D 5 sec answer.
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Re: What is the volume of the cube above?  [#permalink]

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New post 07 Oct 2015, 04:16
Reequired: Volume of the cube

A cube has all the sides equal and each surface is a square. Hence if we find the side of the cube, we can find the volume

Statement 1:
Surface are of the cube is 600 square inches

Total surfaces of a cube = 6.
Total surface area = 600.
Hence area of one side = 100.

Therefore the side = 10
Volume of cube = (Side)^3 = 1000
SUFFICIENT

Statement 2:
AB = \(10 \sqrt{3}\)

Diagonal of a cube = \(\sqrt{3}\)*side
Hence we have side = 10
Volume = (Side)^3 = 1000
SUFFICIENT

Option D
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Re: What is the volume of the cube above?  [#permalink]

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New post 26 May 2016, 15:22
we have find volume of given cube

Statement 1 gives information about the total surface area of the cube = 600 sq.inches
we know that cube has 6 equal faces area of single face = 100 which in turn gives us the side as 10 inches
Volume of cube = 1000 cu.inches
So sufficient

Statement 2 gives the length of longest diagonal of the cube as 10 *\(\sqrt{3}\)
this in turn gives us the side as 10 inches
Volume of cube = 1000 cu.inches
So sufficient

Correct Answer - D
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Re: What is the volume of the cube above?  [#permalink]

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New post 17 Jul 2016, 00:33
monirjewel wrote:
Attachment:
1026203817.jpg
What is the volume of the cube above?

(1) The surface area of the cube is 600 square inches
(2) The length of diagonal AB is \(10\sqrt{3}\) inches


ANSWER IS D since each statements are sufficient alone on their own .

(1) The surface area of the cube is 600 square inches
\(6a^2=600\)

a=10
\(V=a^3==>10^3\) =1000 Units
SUFFICIENT

(2) The length of diagonal AB is \(10\sqrt{3}\) inches
\(d=a\sqrt{3}\)
\(a\sqrt{3}=10\sqrt{3}\)

a=10
\(V=10^3\)

SUFFICIENT

BOTH SUFFICIENT ALONE
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Re: What is the volume of the cube above?  [#permalink]

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New post 05 Sep 2017, 17:51
monirjewel wrote:
Attachment:
1026203817.jpg
What is the volume of the cube above?

(1) The surface area of the cube is 600 square inches
(2) The length of diagonal AB is \(10\sqrt{3}\) inches


St 1

Basic formula =2lw +2wh +2lh

Because the shape is a cube l=w=h

suff

St 2

Just apply pythagorean theorem to find the height of the square

D
Re: What is the volume of the cube above? &nbs [#permalink] 05 Sep 2017, 17:51
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