# Thread: Volume of a torus

1. ## Volume of a torus

Consider a torus that is formed by rotating a circle of radius a, initially lying in the x-z-plane, about the z-axis in such a way that its centre describes a circle of radius A.

a) Explain how you would set up the volume integral of the torus in spherical polar co-ordinates and hence evaluate this.

b) Express as a triple integral the moment of inertia of the torus about the z-axis .

2. I've now read somewhere that

V = Int{a,-a}Int{pi,-pi}Int{A+sqrt(a^2-z^2),A-sqrt(a^2-z^2)} * rho drho dtheta dz

where the limits of the integral are in { }.

Still can't see how this has been constructed though.