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

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

by AAPL » Sat Nov 25, 2017 9:12 am
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

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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by EconomistGMATTutor » Sat Nov 25, 2017 9:42 am
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

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
Hi AAPL,
Let's take a look at your question.

We know that a volume of a sphere with radius x can be represented as:
$$V=\frac{4}{3}\pi x^3$$

If the length of this radius is doubled, the radius will become 2r and the volume V1 will be:
$$V_1=\frac{4}{3}\pi\left(2x\right)^3$$
$$V_1=\frac{4}{3}\pi\left(8x^3\right)$$
$$V_1=8\times\frac{4}{3}\pi x^3$$
$$V_1=8V$$

It means that the resultant volume is 8 times larger than the original volume.
Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.
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