# calculus

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A right triangle with hypotenuse 5 inches is revolved around one of its legs to generate a right circular cone. Find the radius and height of the greatest volume cone.

• calculus -

v = 1/3 pi r^2 h

r^2 + h^2 = 25

v = 1/3 pi (25-h^2)h = 1/3 pi (25h - h^3)

a max/min occurs when dv/dh = 0:

25 - 3h^2 = 0
h = 5/√3
r = 5√2/√3

It's a max because v'' < 0

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