Geometry

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sunsphere314: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Mon Mar 21, 2011 1:56 pm

by sunsphere314 » Wed Sep 07, 2011 12:56 pm

Would someone please explain?

A cylinder has a surface area of 360 pi, and is 3 units tall. What is the diameter of the cylinder's circular base?

a) 8 b)12 c)16 d) 20 e)24

Thank You!

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Source: Beat The GMAT — Problem Solving | Wed Sep 07, 2011 12:56 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Sep 07, 2011 1:52 pm

the surface area of cylinder is 2pi*rh + 2pi*r^2, hence 2pi(rh+r^2)=360*pi or rh+r^2=180

now we can solve quadratics by allowing r to be variable ==> r^2+hr-180=0
from the condition given in the problem h=3 and r^2+3r-180=0,
r(1,2)=(-3 +- sqr{9+ 4*180})/2=(-3 +- 27)/2; r(1)=12 and r(2)=-15

we can have only positive radius, hence r=12 and diameter 2r=24

e

sunsphere314 wrote:Would someone please explain?

A cylinder has a surface area of 360 pi, and is 3 units tall. What is the diameter of the cylinder's circular base?

a) 8 b)12 c)16 d) 20 e)24

Thank You!

Success doesn't come overnight!

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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Thu Sep 08, 2011 5:41 am

Agree ANs must be 12

This time no looking back!!!
Navami

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