# Maximum volume

• Mar 16th 2013, 12:55 AM
jellchavez
Maximum volume
A sector with central angle (theta) is cut from a circle of radius 12 inches and the edges of the sector are brought together to form a cone. Find the magnitude of theta such that the volume of the cone is a maximum.
• Mar 16th 2013, 01:25 AM
princeps
Re: Maximum volume
Quote:

Originally Posted by jellchavez
A sector with central angle (theta) is cut from a circle of radius 12 inches and the edges of the sector are brought together to form a cone. Find the magnitude of theta such that the volume of the cone is a maximum.

$s=12$

$2r\pi=\frac{s\pi\theta}{180}$

hence

$r=\frac{s\theta}{360}$

$V=\frac{r^2 \pi H}{3}$ and $H=\sqrt{s^2-r^2}$

Now , find $\theta$ from $V'_{\theta}=0$