Question

This problem is confusing me. I don't know how to do this without an equation.

Use spherical coordinates to find the volume between 2 hemispheres p=3 and p=6. Think of the smaller hemisphere being inside the bigger one.

Answer 1

Volume of larger hemisphere - Volume of smaller hemisphere = Area between.

Answer 2

what's p?

Answer 3

Yes but I'm supposed to do it by integration which I don't see how that is possible if I'm only given the radius which is p from spherical coordinates.

Answer 4

Is p the magnitude

Answer 5

I'm assuming p is from spherical coordinates of p rho and theta

Answer 6

Not sure then.. maybe if p was the radius

Answer 7

Well p would be the radius since it's the distance from the origin

Answer 8

Spherical co-ords are r, theta and phi, no p.

If p is the radius r then it's quite straightforward.
Volume of a hemisphere is 2/3pi.r^3

so we just go 2/3pi6^3 - 2/3pi3^3 for the volume between two hemispheres

Answer 9

No integration required

Answer 10

^

Answer 11

You could also double integral for 2 hemispheres or spheres but yea..

Answer 12

That's what I'm supposed to do but I don't know how to go about it