Arclength and Surface Area Example Suppose that you want to design a ski lift and need to determine how much cable will be needed between two posts that are 66 feet apart. The formula for the cable is y = 50 cosh(x/50) To compute the length of the cable we cut the cable into many pieces and the length of each piece is approximately equal to
Multiplying by (Dx)^{2}/(Dx)^{2} gives
Taking a limit as Dx goes to zero
and adding up all the pieces, we arrive at
= 70.9 feet Surface Area of Revolution
The area of a frostum is
If we revolve a curve around the xaxis, we have that the surface area of
revolution is given by
Set up an integral that gives the surface area of revolution about the x axis of the curve We find
