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Cube A has a volume of a cubic inches. If each side of Cube B is twice

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Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 13 Sep 2017, 21:49
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Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a

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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 13 Sep 2017, 22:35
Volume of cube= L^3

Volume of cube A= a cubic inches
a= L^3
L= a^1/3

Side of cube B is twice as long as side of A.
Side of Cube B= l= 2*(a^1/3)

Volume of Cube B= l^3
= 2^3 * (a^1/3)^3
=8*a

Hence Answer is option D.

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Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post Updated on: 13 Sep 2017, 22:48
Bunuel wrote:
Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a

Volume of Cube A = a = \(s * s* s\).

Cube B = (2s * 2s * 2s), or 8(s * s * s)

Substitute a for (s * s * s): volume of Cube B = 8a

OR

Let Cube A have sides = 1.
Volume is (1*1*1) = a

Each of Cube B's sides is twice as long as Cube A's sides.
Cube B has sides = 2.

Volume of B is
(2*1) * (2*1) * (2*1), or
(2*2*2)(1*1*1).
Substitute a for (1*1*1):
(2*2*2)(a) = 8a, is volume of Cube B

Basically: For dilation, to get resultant volume, multiply the volume of the original by the multiplier cubed -- because each length is scaled up by the multiplier, and volume = (length * length * length).

Multiplier is 2
2\(^3\) = 8

Volume of Cube A = a, so
volume of Cube B = 8a

ANSWER D
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Originally posted by generis on 13 Sep 2017, 22:37.
Last edited by generis on 13 Sep 2017, 22:48, edited 1 time in total.
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 13 Sep 2017, 22:47
let a = 8
side of cube A = 2
each side is twice the side of A = 4*4*4, vol = 64
That is 8a
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 13 Sep 2017, 23:10
Bunuel wrote:
Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a



The volume of the cube A is a cubic inches, the side of the cube is \(\sqrt[3]{a}\) inches.
If the side of cube B is twice as long, the side must be 2 \(\sqrt[3]{a}\).

The volume of the cube B must be \((2\sqrt[3]{a})^{3}\) which is 8a(Option D)
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 14 Sep 2017, 02:23
Let side of Cube A = x.
As volume of A = a=> \(x^3 =a\)

Now Cube b side = 2* side of A = 2*x
Volume of b \(= (2x)^3 = 8x^3 = 8a\) .. as\(x^3 =a\)

Answer:D
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 14 Sep 2017, 04:27
Bunuel wrote:
Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a


Volume of a cube = Side^3

If you double the side, the volume will become 2^3 = 8 times.

Hence volume of cube B is 8a.

Answer (D)
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 14 Sep 2017, 09:44
Correct me if I am wrong. Let the volume of cube B,
A/V = A^3/8A^3
Therefore, V= 8A
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice  [#permalink]

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New post 18 Sep 2017, 05:46
Bunuel wrote:
Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a


We can let the side of cube A = x and the side of cube B = 2x. Since the volume of cube A is a, we have x^3 = a. Then, the volume of cube B is (2x)^3 = 8x^3. Substituting a for x^3, we obtain 8a for the volume of cube B.

Answer: D
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Re: Cube A has a volume of a cubic inches. If each side of Cube B is twice &nbs [#permalink] 18 Sep 2017, 05:46
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