# MvCalc49

From Example Problems

Let the center of the sphere be at the origin and let the axis of the hole be along the z-axis. The volume V of the sphere is and that of the circular hole is obtained as follows.

Volume of the upper half of the hole= where z is obtained from the equation and R is the circle in the XY-plane,that is .Hence,the volume V1 of the circular hole is

where R is given by . Changing into polar coordinates,we obtain,

Hence the remaining portion =