MvCalc49
From Exampleproblems
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,
![v_1=2\int_{0}^{2\pi}\int_0^b \sqrt{a^2-r^2} r dr d\theta=\frac{4\pi}{3}[a^3-(a^2-b^2)^{\frac{3}{2}}]\,](/wiki/images/math/3/b/b/3bb8886ea9629adac98b94c49a786178.png)
Hence the remaining portion =![V-V_1=\frac{4\pi}{3}a^3-\frac{4\pi}{3}[a^3-(a^2-b^2)^{\frac{3}{2}}]=\frac{4\pi}{3}(a^2-b^2)^{\frac{3}{2}}\,](/wiki/images/math/a/f/f/aff387d0f54554efbea3abafc2903fff.png)
