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.

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

Volume = πr^2h

Volume = πr^2(r)

= πr^3

= π(5)^3

= 125π

Hence Volume = 125π units

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