A cylindrical drill with radius 2 is used to bore a hole throught the center of a sphere of radius 7. Find the volume of the ring shaped solid that remains using polar coordinates.© BrainMass Inc. brainmass.com March 4, 2021, 6:14 pm ad1c9bdddf
The figure above is a simple version of how the solid looks. The hole is drilled from top to bottom. Let the radius of the sphere = W and that of the drill = w.
In order to simplify things, align the center of the sphere with the origin (0,0,0) and the axis of the cylindrical hole is aligned with the z-axis, so that the equation of the sphere is
x2 + y2 + z2 = W2 and the equation of the cylindrical hole is x2 + y2 = w2.
So if you look at the xy-plane (i.e. z = 0), we ...
Polar coordinates are used to find the volume of a Ring-Shaped solid. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.