Question

a spherical balloon is being inflated find the instantaneous rate of change of the surface area s of the balloon

Answer 1

the rate of increase of surface area of the balloon is a) 16π b) 24π c) 48π

I found the complete question on Study.com, which is

A spherical balloon is being inflated. Find the rate of increase (with respect to the radius r) of the surface area (S=4πr2) when:

a) r=2 inches

b) r=3 inches

c) r=6 inches

Area of a spherical balloon is S = 4πr2. So the increasing rate of area of the balloon with respect to the radius r is

dS/dr = 8πr

Therefore, the rate of increase of the surface area

a) 16π

b) 24π

c) 48π

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