# ap Calculus

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A right circular cone has a fixed slant height, s= 12 inches. Determine the radius and the height of the cone with maximum volume

• ap Calculus -

volume of cone is

V=4/3(pi)r^2h

s^2=r^2+h^2 or s^2-h^2=r^2

V=4/3(pi)(s^2-h^2)h

if 4/3(pi)=k

V=k(144-h^2)h

V=144kh-kh^3

volume is a max when dV/dh is zero

dV/dh = 144k-3kh^2

144k-3kh^2 = 0

144k = 3kh^2
48=h^2

this gives you h, from which you can find r from

s^2-h^2=r^2

• ap Calculus -

I am sure that Dr Russ meant to type

volume of cone is

V=1/3(pi)r^2h

• ap Calculus -

Yes oops!

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