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The surface area of a sphere is 4Ï€R^2, and the...

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by BTGmoderatorLU » Fri Nov 17, 2017 11:27 am
The surface area of a sphere is 4πR^2, and the volume of a sphere is (4/3)·π·R^3, where R is the radius of the sphere. If the volume of a certain sphere is double the surface area of that sphere, what is the radius of that certain sphere?

A. 1.5
B. 6/Ï€
C. 1.5Ï€
D. 6
E. 6Ï€

The OA is D.

Please, can any expert assist me with this PS question? I'm really confused with it, how can I solve it? Thanks in advanced.
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by [email protected] » Fri Nov 17, 2017 11:35 am
Hi LUANDATO,

While this question might 'look scary', you can actually just set up one equation and simplify it to get the correct answer:

We're given a few facts to work with:
1) The surface area of a sphere is 4Ï€R^2
2) The volume of a sphere is (4/3)·π·R^3
3) The volume of a certain sphere is DOUBLE the surface area of that sphere

We're asked for the radius (R) of that sphere. The equation we can set up is...

(4/3)(Ï€)(R^3) = (2)(4)(Ï€)(R^2)
(4/3)(R) = 8
R = (8)(3/4)
R = 24/4 = 6

Final Answer: D

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by EconomistGMATTutor » Sat Nov 18, 2017 2:22 pm
The surface area of a sphere is 4πR^2, and the volume of a sphere is (4/3)·π·R^3, where R is the radius of the sphere. If the volume of a certain sphere is double the surface area of that sphere, what is the radius of that certain sphere?

A. 1.5
B. 6/Ï€
C. 1.5Ï€
D. 6
E. 6Ï€

The OA is D.

Please, can any expert assist me with this PS question? I'm really confused with it, how can I solve it? Thanks in advanced.
Hi LUANDATO,
Let's take a look at your question.

$$Area=\ 4\pi R^2$$
$$Volume=\frac{4}{3}\pi R^3$$

The question states:
"If the volume of a certain sphere is double the surface area of that sphere", we can write it as:
$$Volume=2\times Area$$
$$\frac{4}{3}\pi R^3=2\times\left(4\pi R^2\right)$$
$$\frac{1}{3}\pi R=2\times\left(\pi\right)$$
$$\frac{1}{3}R=2$$
$$R=2\times3$$
$$R=6$$

Therefore, radius of the sphere is 6.
Hence, Option D is correct.

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