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tsmith93: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Fri Feb 19, 2010 12:36 pm; Location: Pennsylvania; Thanked: 1 times

spheres

by tsmith93 » Fri Mar 26, 2010 5:38 am

Three identical balls fit snugly into a cylindrical can: the radius of the spheres equals the radius of the can, and the balls just touch the bottom and the top of the can. If the formula for the volume of a sphere is V=4/3(pi)r^3, what fraction of the volume of the can is taken up by the balls?

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Source: Beat The GMAT — Problem Solving | Fri Mar 26, 2010 5:38 am

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 am; Thanked: 32 times; Followed by:1 members

by eaakbari » Fri Mar 26, 2010 5:53 am

Volume of one sphere = 4/3 *pi*r^3
Volume of 3 spheres is = 4 *pi*r^3
Volume of cylinder is pi*r^2 h
Here h is 6 r as balls fit snugly into cylinder

Therefore vol of 3 spheres / vol of cylinder = 4/6 = 2/3

Answer = [spoiler]2/3[/spoiler]