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A sphere has a radius of x units. If the length of this radius is doub

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Bunuel
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A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   05 Dec 2014, 07:41
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Tough and Tricky questions: Geometry.



A sphere has a radius of x units. If the length of this radius is doubled, then how many times larger, in terms of volume, is the resultant sphere as compared with the original sphere?

A) 1
B) 2
C) 4
D) 8
E) 16

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Source: Chili Hot GMAT
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D
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VladimirKarpov
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   05 Dec 2014, 08:53
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Volume of the sphere = (4/3)*pi*r^3
New volume = (4/3)*pi*(2r)^3 = (4/3)*pi*8r^3

8 times larger
Answer: D
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   05 Dec 2014, 10:25
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All we need to know is that the volume of a sphere is linearly proportional or directly related to the cube of its radius. So if we double the radius, the actual volume increases by a factor of 2^3 or 8.

Choice D
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   05 Dec 2014, 23:42
A sphere has a radius of x units. If the length of this radius is doubled, then how many times larger, in terms of volume, is the resultant sphere as compared with the original sphere?

A) 1
B) 2
C) 4
D) 8
E) 16


\(\frac{Volume-of-the-sphere-with- radius-2x-units, double-the-radius-of-original-sphere}{Volume-of-the-original-sphere-with-radius-x-units}\)

= \((\frac{4}{3}*\Pi*(2x)^3)/(\frac{4}{3}*\Pi*(x)^3)\)

= \(\frac{8x^3}{x^3}\)

= 8 => volume of the resultant sphere will be 8 times larger than that of original sphere

Answer: D
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   06 Dec 2014, 07:27
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The radius is x.
volume of a sphere= 4/3 pi r*r*r. In this case r=x. now if x is doubled then x=2x so x*x*x=8x*x*x
so new volume becomes 8 times the volume.
Hope this one helps.
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   08 Dec 2014, 06:10
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Bunuel wrote:

Tough and Tricky questions: Geometry.



A sphere has a radius of x units. If the length of this radius is doubled, then how many times larger, in terms of volume, is the resultant sphere as compared with the original sphere?

A) 1
B) 2
C) 4
D) 8
E) 16

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is D.
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   08 Dec 2014, 19:16
Answer = D) 8

Volume of sphere \(= \frac{4}{3} \pi r^3\)

\(If x = 1, r^3 = 1\)

\(If x = 2, r^3 = 8\)

Increase would be 8 times
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   14 Aug 2015, 06:02
Bunuel wrote:

Tough and Tricky questions: Geometry.



A sphere has a radius of x units. If the length of this radius is doubled, then how many times larger, in terms of volume, is the resultant sphere as compared with the original sphere?

A) 1
B) 2
C) 4
D) 8
E) 16

Kudos for a correct solution.

Source: Chili Hot GMAT

r becomes 2r
r^3 becomes 8r^3
Hence, 8 times.
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink] New post   22 Sep 2023, 16:28
I did not know the volume of a sphere equation off hand. I assume that test takers often forget equations, especially during crunch time.

I was able to reason that 2X^2(Pi)/X^2(Pi) = 4. Thus cancelling out A, B, and C. Then from there I had a choice to make between D & E. I like those odds even if I forget an EQN, 50/50 is better than 20/100. I chose D based on the fact that a circle is 2D and that it was more likely that X^3 would get me to a sphere than X^4.

A creative way to get there I'm sure, but I'm trying to stay flexible and creative to get to answers quickly.
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Re: A sphere has a radius of x units. If the length of this radius is doub [#permalink]
22 Sep 2023, 16:28
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