Question

The surface area of a right circular cylinder of height 2 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 = 3.

24π
64π
20π
16π

Answer 1

S(r) = 2pi*r*h + 2pi*r^2

S ' (r) = 2pi*h + 2*2*pi*r .... differentiate with respect to r

S ' (r) = 2pi*h + 4pi*r

S ' (3) = 2pi*h + 4pi*3 ... plug in r = 3

S ' (3) = 2pi*h + 12pi

S ' (3) = 2pi*2 + 12pi .... plug in h = 2

S ' (3) = 4pi + 12pi

S ' (3) = 16pi

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Answer: D) 16pi