01
Surface area: revolved cubic
The curve
over is revolved around the -axis. Find the area of the resulting surface.
02
Surface area: cone
A cone may be described as the surface of revolution of a ray emanating from the origin, revolved around the
-axis. Let
for some . Find the surface area of the cone given by revolving the graph of around the -axis over . Can you also calculate this area using geometry? And verify the two methods give the same formula? (Hint: ‘unroll’ the cone into a sector.)
03
Surface area: parabolic reflector
A parabolic reflector is given by rotating the curve
around the -axis for . What is the surface area of this reflector?
04
Surface area: torus
A torus is created by revolving about the
-axis the circle with this equation: Find the surface area of this torus.
(Hint: compute for the top and bottom of the circle separately and add the results.)
