Spherical coordinates: Find the mass of a solid inside a....

[pakman]

Find the mass of a solid inside a sphere of radius 2a and outside a circular cylinder of radius a whose axis is a diameter of the sphere, if the density is proportional to the square of the distance from the center of the sphere.

So I'm imagining a sphere, let's say centered around xyz = 0. Then a cylinder comes into play, which it seems to me like it has the same radius as the sphere. However, I'm not sure what it means by saying "whose axis is a diameter of the sphere."

 

[mark07]

Re: Spherical coordinates

Then a cylinder comes into play, which it seems to me like it has the same radius as the sphere.

Radius of the cylinder is given to be half that of the sphere!

You have a spherical iron ball, let's say, and you are making a hole through the center with a cylinder. The remaining solid looks somewhat like a weird wedding ring??

Like you said, consider a sphere centered at the origin with radius 2a. Let's say the cylinder is along z-axis (then the axis of the cylinder is z-axis which contains a diameter of the sphere).

Equation of the sphere: \(\displaystyle \L x^2 + y^2 + z^2 = 4a^2\)

Equation of the cylinder: \(\displaystyle \L x^2 + y^2 = a^2\)

The solid lies between them. Find the mass of the part of the solid in the first octant and multiply by 8, since it's easier to set it up that way.