Sphere Volume

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mariah: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Aug 05, 2008 3:28 pm; Thanked: 2 times

by mariah » Sun Nov 28, 2010 4:15 am

Sphere Volume Formula: V=4/3*pi*r^3
The surface area of a sphere: S= 4*pi*r2

In terms of S, V=?

oa given is [spoiler]Sr/2[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sun Nov 28, 2010 4:15 am

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Sun Nov 28, 2010 6:15 am

I'm sorry, but that doesn't seem right. Plug in S into your OA and see if you reach V=4/3*pi*r^3 :

Sr/2 = 4*pi*r2 *r/2 = 2*pr*r^3 (the 4 and the 2 reduce to leave 2) which is not equal to the Volume formula.

in order to get from S=4*pi*r2 to V=4/3*pi*r^3 :, we'd need to take S and:
1) Multiply by r (to get r^3)
2) divide by 3 (to get the 4/3).

Thus, the answer should be Sr/3.

Geva
Senior Instructor
Master GMAT
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https://www.mastergmat.com

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rishab1988: Master | Next Rank: 500 Posts; Posts: 332; Joined: Tue Feb 09, 2010 3:50 pmFollowed by: 7 members; Thanked: 41 times; GMAT Score:720

by rishab1988 » Sun Nov 28, 2010 9:11 am

My approach was very straight forward:

V = 4/3 *pi *r^3 or (4*pi*r^2)r/3 right?
= Sr/3 [just substituted S for 4pi r^2]

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