problem 254 mathcounts

Mathematics
Tutor: None Selected Time limit: 1 Day

A cylinder's radius is equal to its height. If the surface area is 100 pi units squared, what is its volume? Express your answer in terms of pi.

Oct 19th, 2014

r = h

Surface area = 100 pi units

V = ?

Now 

Surface area = 2πrh+2πr^2

             100 π  = 2πr(r)+2πr^2

             100 π = 2πr^2 + 2πr^2

             100 π = 4πr^2

              100 = 4 r^2

               25 = r^2

            √25 = √r^2

               5 = r

Now 

Volume = πr^2h

Volume = πr^2(r)

             = πr^3

             = π(5)^3

             = 125π

Hence Volume = 125π units

Oct 19th, 2014

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