# Thread: optimization - cone inscribed in a sphere

1. ## optimization - cone inscribed in a sphere

A right circular cone is inscribe in a sphere of radius 15cm. Find the dimensions of the cone that has the maximum volume.

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Are my equations correct? I can't seem the get the right answers.

h= height of the cone

?

2. Originally Posted by shawli
A right circular cone is inscribe in a sphere of radius 15cm. Find the dimensions of the cone that has the maximum volume.

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Are my equations correct? I can't seem the get the right answers.

h= height of the cone

?
did you make a sketch on a set of axes?

$\displaystyle h = R+y$

$\displaystyle r = x$

$\displaystyle V = \frac{\pi}{3} x^2 (R+y)$

$\displaystyle V = \frac{\pi}{3} x^2(R +\sqrt{R^2-x^2})$

find $\displaystyle \frac{dV}{dx}$ and maximize

3. ## Re: optimization - cone inscribed in a sphere

A right circular cone is inscribed in a sphere of radius 15cm. find the dimensions of the cone that has the maximum volume. Please Help.