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Surface Area of a Cylinder

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Surface Area of a Cylinder

by C » Sat Mar 20, 2010 10:24 pm
A cylinder has a surface area of 360(PI), and is 3 units tall. What is the diameter of the cylinder's circular base?


This is a problem from MGMAT Geometry. There were no answer choices, only an explanation that I did not understand.

Can anyone help me explain this one?

Thanks guys.
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by rockeyb » Sat Mar 20, 2010 10:33 pm
C wrote:A cylinder has a surface area of 360(PI), and is 3 units tall. What is the diameter of the cylinder's circular base?


This is a problem from MGMAT Geometry. There were no answer choices, only an explanation that I did not understand.

Can anyone help me explain this one?

Thanks guys.
Surface area is give = 360(PI)

Surface area of cylinder = 2(PI) r^2 h .

r = radius

h = height , given =3

360(PI) = 2 (PI) r^2 x 3

360/6 = r^2

60 = r^2

r = 2 root (15)

Diameter = 4root (15).

whats the OA ?
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by this_time_i_will » Sat Mar 20, 2010 11:48 pm
Surface area = 2*Pi*r *(h+r)

2*pi*r*(3+r) = 360*Pi
Solving, we get following quadratic equation:
r^2+3r-180 = 0
(r+15)(r-12)=0
so, r = 12 or r = -15.

Taking r = 12, we have diameter as 24.
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