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Who wants to do some math?

speg

speg

Diamond Member
Ugh, calculus test tommorrow :frown:

A sphere of radius 4 cm is inscribed in a right circular cone. What is the least possible vlume of the cone?

Alright, so this are the equations I got. One of them is wrong, becasue I can't get the right answer.

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

So I find h in terms of r, and come out with ( Im not sure if this is right ) :

h = 4r/(r-4)

Plug that into the volume equation, take the derivative, set to 0 and I get:
r=6
therefore: h=12
therefore: V= 452.4

But, the back of the book says V = 536.17
 
Hmm, when I graph the function: f(x)=4pix^3(3x-12)^(-1) I get the minimum at 452. So either my equation for the height is wrong, or the back of the book is wrong.... *shrug*
 
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