Question

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4.

24π
16π
64π
20π

Answer 1

You have to take the derivative of the function S(r) respect to the radius.

2, π and h are constants, so:

d [S(r)] / dr = 2πh + 4πr = 2π [h + 2r]

h = 4 , r = 4 => d [S(r) ] / dr = 2π [4 + 8] = 24π

Answer: 24π