# Multiple integrals

1. Feb 28, 2004

### nas

if i have a hemisphere of radius 4, is it possible using multiple integration for me to find the radius of a cylinder that sits inside the hemisphere such that the vol inside the hemisphere and outside the cylinder is a 1/12 of the vol of the hemisphere
anyone that can help me on this-i respect you
my inital thoughts were do i do this via polar cordinates-but the hgt of the cylinder is causing me problems-or do i assume hgt is also the radius of the cylinder?

2. Feb 28, 2004

### matt grime

I suppose so, but it seems very unneccesary.

let r be the radius of the cylinder - find it's height in terms of r (it touches the surface of the sphere presumably) You can now find the volume of the cylinder in terms of r. Find the r that satisfies the criterion you gave using simple algebra (you know the volume of the sphere too).