- #1
squeeky
- 9
- 0
Homework Statement
Use Cylindrical Coordinates.
Find the volume of the solid that the cylinder [tex]r=acos\theta[/tex] cuts out of the sphere of radius a centered at the origin.
Homework Equations
Sphere = x2+y2+z2=a3
The Attempt at a Solution
I think that the limits are from -pi/2 to positive pi/2 for theta, 0 to acos(theta) for r, and negative (a3-r2)1/2 to positive (a3-r2)1/2. This gives me the equation:
[tex]\int^{\pi/2}_{-\pi/2}\int^{acos\theta}_0\int^{\sqrt{a^3-r^2}}_{-\sqrt{a^3-r^2}} dzrdrd\theta[/tex]
Solving this, I get a volume of [tex]\frac{4\pi}{3}a^{9/2}+\frac{8}{9}a^3[/tex]
But is this right?