Volume vs Area of Sphere

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hijazim: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sun Feb 22, 2009 11:27 pm; GMAT Score:600

by hijazim » Sun Mar 01, 2009 6:30 am

This question has a wording problem. If I am not wrong the volume should be 4/3*pi*r^3 and not 4/3*pi*r^-3.

Any help please. The OA is D. But I couldn't interpret how???

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Source: Beat The GMAT — Data Sufficiency | Sun Mar 01, 2009 6:30 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sun Mar 01, 2009 6:39 am

You are right, that (-3) does not belong there. It may be a typo, it's surely not correct. Check Wikipedia when in doubt!

Now, back to the question: it says here that the volume of the sphere is 972Pi, which will be (4/3)*Pi*(r^3):
972 = 1000 - 28 = 4*250 - 4*7 = 4*243
So you have that (4/3)*(r^3) = 4*243
This makes r^3 = 243*3 = 729 or 9^3, making r = 9.

This means that the total surface area will be 4Pi(r^2) = 4*81*Pi = 324Pi.
Since my answer is consistent with the OA, it was indeed just a typo.

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hijazim: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sun Feb 22, 2009 11:27 pm; GMAT Score:600

by hijazim » Sun Mar 01, 2009 6:57 am

Yes man, this is it. Thanks for sharing

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