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Calculus III?
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)
1 Answer
- Anonymous1 decade agoFavourite answer
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.