A watchdog is tied to the outside wall of a round building 20 feet in diameter. If the dog's chain is long enough to wind half way around the building, how large an area can the watchdog patrol?
(In reply to WD-40 please! - spoilers
Re:"So now donít I just integrate S(theta) dtheta from theta = 0 to theta = 180? Is this idea wrong, or is my following integration wrong?"
What is being added to the area are little (infinitesimal) triangles with height S and base S*dtheta, so each area would be (S^2)/2 dtheta, not S dtheta. You could even ignore the division by two to allow for both horns and not have to multiply at the end by 2.
I didn't read the rest, but am leery of mixing degree angular measure in a calculus problem, where you need radians.
Posted by Charlie
on 2004-10-28 15:27:33