A hole is cut through the center of a sphere of radius r.

A hole is cut through the center of a sphere of radius r. The height of the remaining spherical ring is h. Find the volume of the ring (two ways), and show that it is independent of the radius of the sphere. (See problem 4, page 505.) (a) as a A????1dxA????1 integral. (b) as a A????1dyA????1 integral.

[2] Set up and evaluate the definite integral that gives the length of the graph of f(x)=(e^3x+e^-3x)/6 over the interval 0 ln 2 ? ?x .

[3] Set up and evaluate the definite integral that gives the surface area of a sphere of radius a. (I suggest taking the curve x^2+y^2=a^2 about the x-axis.)