The perimeters of the ends of a frustum are 48cm and 36cm. If the height of the frustum be 11cm, find its volume.
Let r1 and r2 be the radii of the circular ends of the frustum and h be its height. Then,
2πr1=48,2πr2=36;h=11cm⇒r1=24π,r2=18π;h=11cm
Let V be the volume of the frustum. Then
V=13π(r21+r22+r1r2)h
⇒V=13×π×11×{(24π)2+(18π)2+24π+18π}
⇒V=13×π×11×576+324+432π2cm3=113×133222×7cm3=1554cm3