Expert: Abe Mantell - 5/29/2005

Question
i found this question in a website. though it has an answer there, i don't really understand it.

A hole is made in a sphere passing through its center. Imagine that the removed part is formed by two opposite spherical bowls with a cylinder between them. The question is: Knowing the length of the cylinder is 6cm, what is the residual volume of the sphere?

the answer given is:
The remaining volume, v, is given by:
v = 4/3 pi (L/2)^3
where L is the length of the cylindrical hole (= 6 cm).
v = 36 pi cubic centimetres.  

Answer
Hello Celes,

Interesting question!

Since the radius of the sphere is not given, it must
not matter!  Thus, imagine the diameter is equal to the
length of the cylinder!  So that the cylinder "removes"
has zero volume!  Thus, the sphere has a radius of 3 cm...
with a volumeee of (4/3)Pi*3^3=36Pi

OK?

Abe