Posted by Macy on .
Let R be the square region bounded by y = 2, x = 2, and the
x and yaxes. When R is rotated about the xaxis, what is the volume of the
resulting solid? What is the volume of the solid generated by rotating R about
the yaxis?

Calculus 
Steve,
first, since it's a square, it does not matter which side is used as the rotational axis.
geometrically, we have a cylinder of height=2, radius=2
v = pi * 2^2 * 2 = 8pi
Analytically,
v = Integral(pi y^2 dx)[0,2]
= Integral(4pi dx)[0,2]
= 4pi x[0,2]
= 8pi