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# If the volume of the cube above is 64 cubic centimeters, what is the

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Math Expert
Joined: 02 Sep 2009
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If the volume of the cube above is 64 cubic centimeters, what is the  [#permalink]

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18 Jan 2018, 03:10
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Difficulty:

35% (medium)

Question Stats:

82% (00:36) correct 18% (01:24) wrong based on 60 sessions

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If the volume of the cube above is 64 cubic centimeters, what is the shortest distance, in centimeters, from point A to point B?

A. $$4\sqrt{2}$$

B. $$4\sqrt{3}$$

C. $$4\sqrt{6}$$

D. $$8\sqrt{2}$$

E. $$8\sqrt{3}$$

Attachment:

2018-01-18_1409.png [ 3.79 KiB | Viewed 1469 times ]

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Re: If the volume of the cube above is 64 cubic centimeters, what is the  [#permalink]

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18 Jan 2018, 04:48
Bunuel wrote:

If the volume of the cube above is 64 cubic centimeters, what is the shortest distance, in centimeters, from point A to point B?

A. $$4\sqrt{2}$$

B. $$4\sqrt{3}$$

C. $$4\sqrt{6}$$

D. $$8\sqrt{2}$$

E. $$8\sqrt{3}$$

Attachment:
2018-01-18_1409.png

We'll go for Precise since there is an explicit rule that addresses this question.

This doesn't come up too often, but the diagonal of a cube has length $$\sqrt{3}a$$, where a is the length of the side.
Since the volume is 64, then the length of each side is 4 (as 4^3=64) so the length of the diagonal is $$4\sqrt{3}$$

Note - to calculate this, you need to use the Pythagorean theorem twice - once to find the diagonal of the side and the second time to find the diagonal of the cube.
The general equation for the diagonal of a rectangular solid is $$\sqrt{a^2+b^2+c^2}$$ where a,b,c are the lengths of the sides.
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Re: If the volume of the cube above is 64 cubic centimeters, what is the  [#permalink]

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18 Jan 2018, 07:52
Bunuel wrote:

If the volume of the cube above is 64 cubic centimeters, what is the shortest distance, in centimeters, from point A to point B?

A. $$4\sqrt{2}$$

B. $$4\sqrt{3}$$

C. $$4\sqrt{6}$$

D. $$8\sqrt{2}$$

E. $$8\sqrt{3}$$

Attachment:
2018-01-18_1409.png

Sides of the cube is 4 cm

Diagonal of a cube is $$a\sqrt{3}$$ = $$4\sqrt{3}$$ answer will be (B)
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Re: If the volume of the cube above is 64 cubic centimeters, what is the  [#permalink]

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18 Jan 2018, 23:14
a^3= 64
a=4

Diagonal=a(root3)= 4(root3) ans B
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Re: If the volume of the cube above is 64 cubic centimeters, what is the  [#permalink]

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20 Jan 2018, 07:38
Bunuel wrote:

If the volume of the cube above is 64 cubic centimeters, what is the shortest distance, in centimeters, from point A to point B?

A. $$4\sqrt{2}$$

B. $$4\sqrt{3}$$

C. $$4\sqrt{6}$$

D. $$8\sqrt{2}$$

E. $$8\sqrt{3}$$

Attachment:
2018-01-18_1409.png

The diagonal of a cube = side√3, and the shortest distance from A to B is the diagonal.

Since the volume is 64, the side is 4, and the diagonal is 4√3.

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Re: If the volume of the cube above is 64 cubic centimeters, what is the &nbs [#permalink] 20 Jan 2018, 07:38
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