A bucket in the shape of a frustum is OPEN at the top. When calculating the metal sheet used to make it, which area must be left out?

Sheet is needed for the sloping side and for the closed bottom, so the answer is $\pi l(R+r)+\pi r^2$ where $r$ is the bottom radius. The top is an opening, so its circle uses no sheet. Including it is the commonest slip in bucket questions; leaving out the bottom or the curved surface would leave the bucket with a hole or no side at all.