(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Sphere = x^{2}+y^{2}+z^{2}=a^{3}

3. 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 (a^{3}-r^{2})^{1/2}to positive (a^{3}-r^{2})^{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?

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# Homework Help: Cylindrical Coordinates

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