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What is the volume of the cube above?

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monirjewel
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What is the volume of the cube above? [#permalink] 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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D
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Re: Volume of Cube [#permalink] 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: What is the volume of the cube above? [#permalink] 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] New post   20 Jun 2013, 06:23
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Geometry:
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Re: Volume of Cube [#permalink] 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] New post   17 Jul 2016, 00:33
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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] New post   16 Jun 2021, 07:52
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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

Solution:

Question Stem Analysis:

We need to determine the volume of the cube.

Statement One Alone:

Since the cube has 6 faces and its surface area is 600 sq. inches, then each face of the cube has an area of 600/6 = 100 sq. inches. That means each edge of the cube has a length of √100 = 10 inches. Therefore, the volume of the cube is 10^3 = 1,000 cu. inches. Statement one alone is sufficient.

Statement Two Alone:

Since AB is the space diagonal of the cube and the length of the space diagonal of a cube is √3 times the length of the edge of the cube, the edge of the cube has a length of 10√3 / √3 = 10 inches. Therefore, the volume of the cube is 10^3 = 1,000 cu. inches. Statement two alone is sufficient.

Answer: D
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Re: What is the volume of the cube above? [#permalink] New post   07 Oct 2015, 04:16
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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] 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] 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
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Re: What is the volume of the cube above? [#permalink] New post   07 Nov 2020, 08:41
What is the volume of the cube above?

(1) The surface area of the cube is 600 square inches

Area of one side = 100. Side = 10.

Volume = \(s^3 = 10^3 = 1,000\)

SUFFICIENT.
(2) The length of diagonal AB is \(10\sqrt{3}\)

Diagonal of a cube = \(\sqrt{3}\) * 10
Side = \(10\)
Volume = \(s^3 = 10^3 = 1,000\)

Answer is D.
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What is the volume of the cube above? [#permalink] New post   27 Dec 2020, 13:33
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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


The volume of a cube \(= s^3\); where is a side of the cube

(1) Surface area of a cube \(= 6s^2; \ 6s^2=600\); Sufficient.

(2) We see AB of the cube is the largest diagonal. The largest diagonal of \(=s\sqrt{3}; \ s\sqrt{3}=10\sqrt{3}\); Sufficient.

The answer is D
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Re: What is the volume of the cube above? [#permalink] New post   12 Jul 2022, 04:24
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Re: What is the volume of the cube above? [#permalink]
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