# geometry

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A cone has a volume of 36pi cubic meters. Its height is four times its radius. Find the surface area of the cone.

• geometry -

v = 1/3 pi * r^2 * h

h = 4r

36pi = 1/3 pi * r^2 * 4r = 4/3 pi r^3
27 = r^3
r = 3

If you don't include the area of the base,
a = pi * rs = pi * r*sqrt(r^2 + h^2)
= pi * r*sqrt(r^2 + 16r^2)
= pi * r^2 * sqrt(17)
= 116.6 m^2

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