1. ## Optimization Problem about a cone

Find the greatest possible volume for a circular cone having a given slant height??? I don't know how to attempt this

2. 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.

3. Thank you so much that helped a lot!!