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

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

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New post 18 Jan 2018, 03:10
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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
2018-01-18_1409.png [ 3.79 KiB | Viewed 1214 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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New post 18 Jan 2018, 04:48
Bunuel wrote:
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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


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 \(4\sqrt{3}\)
(B) is our answer.

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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New post 18 Jan 2018, 07:52
Bunuel wrote:
Image
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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New post 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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New post 20 Jan 2018, 07:38
Bunuel wrote:
Image
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.

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