A spherical ball of radius 2" is placed in a bowl in the shape of a half-sphere of radius 4". If

the bowl is lled with water to a depth of 3", calculate the volume of water needed.

Hint: Think of the bowl as being described by rotating part of

the circle x^2 + (y-4)^2 = 16 around the y-axis, and the ball as

being obtained by revolving the circle x2 + (y - 2)^2 = 4 around

the y-axis.