A cone was formed by rolling a thin sheet of metal in a form of a sector of a circle 72 cm in diameter with a central angle of 150 deg. Find the volume of the cone.

$\dfrac{c}{150^\circ} = \dfrac{2\pi(36)}{360^\circ}$

$c = 30\pi ~ \text{cm}$

$2\pi r = 30\pi$

$r = 15 ~ \text{cm}$
 

 

$h^2 + 15^2 = 36^2$

$h = \sqrt{1071} \, \text{cm}$
 

$V = \frac{1}{3}\pi r^2 h$

$V = \frac{1}{3}\pi (15^2)\sqrt{1071}$

$V = 7710.91 ~ \text{cc}$