A manufacturer drills a hole through the centre of a metal sphere of radius 5cm. The hole has a radius of 3cm. What is the volume of the resulting metal ring?
I would like to have full solutions to this problem and if possible, directions to how I can draw a diagram. Thank you. Please solve this problem using volumes of revolution.
First step: draw the region i'm talking about.
and to find the limits of integration, you would set the two functions equal to each other and solve for x.
ya I know what you're talking about, I subtracted those too. What I had was the volume of the whole sphere (4/3)(pi)5^3) subtract the volume of the spherical caps (4/3)(pi)3^3) subtract the volume of the cylinder (pi)(3^2)(4).
Since the radius of the hole is 3 cm, I assume the radius of the spherical caps to be 3 cm. And if they're 3 cm, then the height of the cylinder becomes 10-6 = 4.