Find the surface area of the part of the circular paraboloid z=x2+y2 that lies inside the cylinder x2+y2=25.

Parameterize the surface by



with and . Then



so the area is given by the surface integral

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.