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A cube has a volume of T cubic inches . If each side length of the

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A cube has a volume of T cubic inches . If each side length of the  [#permalink]

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New post 18 Aug 2017, 19:56
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A cube has a volume of T cubic inches . If each side length of the cube is doubled , then which of the following is the volumne of this new cube ?

A. 2T in^3
B. 4T in^3
C. 5T in^3
D. 6T in^3
E. 8T in^3

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Re: A cube has a volume of T cubic inches . If each side length of the  [#permalink]

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New post 18 Aug 2017, 22:24
IMO the answer is E.

I did it by picking numbers. Let Volume of Cube be T(old) = 8. Each side of the old cube S(old)= 2. From Stem, Each side of new cube S (new) = 2*2 = 4. New Volume T(New) = 4*4*4 = 64.

T(Old)= 8. T(New) = 64. Substituting in each answer choice we have

A. T(new) = 2*8 = 16. Incorrect
B. T(new) = 4*8 = 32. Incorrect
C. T(new) = 5*8 = 40. Incorrect
D. T(new) = 6*8 = 48. Incorrect
E. T(new) = 8*8 = 64. Correct.

The Answer is E.
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A cube has a volume of T cubic inches . If each side length of the  [#permalink]

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New post 19 Aug 2017, 12:50
Skywalker18 wrote:
A cube has a volume of T cubic inches . If each side length of the cube is doubled , then which of the following is the volumne of this new cube ?

A. 2T in^3
B. 4T in^3
C. 5T in^3
D. 6T in^3
E. 8T in^3

Because volume = length * length * length, you can take the scale factor \(k\) to its third power, \(k^3\) .

You're "scaling up" three lengths by the same factor.

"[E]ach side length doubles" = scale factor 2. 2\(^3\) = 8. Old volume (1)T cu in is now 8T cu in.

Easy to see if original cube has side length 1. Volume = 1 * 1 * 1 = 1 cubic inch. Double the side length. New volume is 2 * 2 * 2 = 8 cu in. So scale factor k\(^3\) is 2\(^3\).

Answer E
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Re: A cube has a volume of T cubic inches . If each side length of the  [#permalink]

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New post 19 Aug 2017, 20:50
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Skywalker18 wrote:
A cube has a volume of T cubic inches . If each side length of the cube is doubled , then which of the following is the volumne of this new cube ?

A. 2T in^3
B. 4T in^3
C. 5T in^3
D. 6T in^3
E. 8T in^3


1. The initial length of the cube : T.
2. New length : T * 2 = 2T.
3. New Volume = 2T * 2T * 2T = 8T^3

E.
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Re: A cube has a volume of T cubic inches . If each side length of the  [#permalink]

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New post 26 Oct 2018, 04:24
Volume of a cube is \(S^3\) = T

Now each side is doubled, so S=2S.

Volume = \((2S)^3\)
= \(8S^3\)
= \(8T\)

OPTION : E
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Re: A cube has a volume of T cubic inches . If each side length of the &nbs [#permalink] 26 Oct 2018, 04:24
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