A lampshade is the frustum of a cone: its wide rim has a radius of 14 cm, its narrow rim a radius of 6 cm, and the vertical distance between the rims is 15 cm. What area of fabric covers its sloping side? (Leave the answer in terms of π.)

First find the slant height, which spans the height and the difference of the radii: $l$ = √$(15^2+(14-6{)}^2)$ = √(225 + 64) = √289 = 17 cm. The curved surface of a frustum is π$(R+r)l$ = π $x20\times 17=340$π sq cm. The trap 300π = π$(R+r)\times 15$ uses the vertical height where the slant height belongs; 136π = π$(R-r)l$ subtracts the radii instead of adding them; 680π = 2π$(R+r)l$ carries over the 2 from a cylinder's 2π$rl$, which the frustum's formula does not have.