Optimization Problem about a cone

**Mathforum** · April 12th 2010, 03:48 PM

Find the greatest possible volume for a circular cone having a given slant height???

I don't know how to attempt this

**skeeter** · April 12th 2010, 04:15 PM

Originally Posted by Mathforum

Find the greatest possible volume for a circular cone having a given slant height???

I don't know how to attempt this

let $s$ = fixed slant height

$r^2 + h^2 = s^2$

$V = \frac{\pi}{3}r^2 h$

$V = \frac{\pi}{3}(s^2-h^2) h$

$V = \frac{\pi}{3}(s^2h-h^3)$

find $\frac{dV}{dh}$ and maximize ... remember that $s$ is a constant.

**Mathforum** · April 13th 2010, 02:39 PM

Thank you so much that helped a lot!!

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