# Math

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Find the radius of a right circular cone if its volume is 1.5 times its lateral area and its radius is half its slant height.

• Math -

a = πrs = πr(2r) = 2πr^2
v = π/3 r^2 h
so,
π/3 r^2 h = 3πr^2
h=9

If s = 2r,
h^2 + r^2 = 4r^2
9+r^2 = 4r^2
r=3

so, r=3 s=6 h=9

check:
a = π*3*6 = 18π
v = π/3 * 9 * 9 = 27π

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