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.
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.
$\displaystyle s=12$
$\displaystyle 2r\pi=\frac{s\pi\theta}{180}$
hence
$\displaystyle r=\frac{s\theta}{360}$
$\displaystyle V=\frac{r^2 \pi H}{3}$ and $\displaystyle H=\sqrt{s^2-r^2}$
Now , find $\displaystyle \theta$ from $\displaystyle V'_{\theta}=0$