Calculus III?

Question

Find the volume of the wrinkled sphere.

Wrinkled sphere
rho = 1 + 0.2 sin(8 theta) sin(phi)

0 <= theta <= 2 Pi)

0 <= phi <= Pi


I need help with my integration.
S(S(S(?,rho,?,?),phi,0,Pi),theta,0,2*Pi)

Answer 1

If you were finding the volume of a normal sphere (rho =a, radius of sphere) the rho limits would just be rho =0 and a.
Wouldn't you just use the wrinkled sphere equation as the upper rho limit?

i.e. S_{phi=0}^{phi=pi}S_{theta=0}
^{theta=2pi}S_{rho=0}
^{rho=1+0.2sin(8theta)sin(phi)}
rho^2*sin(phi) d(rho)d(theta)d(phi).

Don't forget that dV = rho^2*sin(phi) d(rho)d(theta)d(phi) in spherical polar coordinates.