A round hole is drilled through the center of a spherical solid with a radius (r). The resulting cylindrical hole has height 4 cm.

a)What is the volume of the solid that remains?

b)What is unusual about the answer?

Since the radius (R) of the hole isn't given, it must be irrelevant to the solution, i.e., it can take any value in the range 0 to r.

Let's use R=0, in which case the "height" of the hole = diameter of the sphere => 2*r =4. So r = 2.

Therefore, the remaining volume is just the volume of a sphere of radius 2 = 4/3* pi *2^3 = 32 * pi/3.

QED! ;-)