Answered

A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.

AHow fast is the radius of the balloon changing at the instant the radius is 40 centimeters?

___cm/min

BHow fast is the radius of the balloon changing at the instant the radius is 90 centimeters? _____ cm/min

...?

Verified Answer :

Edufirst

Use the chain rule to find the relation between the change in Volume, dV / dt and the change in radius, dr / dt

Change in Volume = dV / dt = [dV / dr] * [dr / dt] => dr / dt = [dV / dt] / [dV/ dr]

Also, Volume, V = [4/3]π(r^3) => dV / dr = 4π (r^2)
And dV/dt = 900 cm^3 / min

Then, dr / dt =  [900 cm^ / min] / [dV/dr] = 900 / [4π r^2] = 225 / (π r^2)

a) r = 40 cm

dr / dt = 225 / [π (40^2) ] = 0.14 cm/min

b) r = 90 cm

dr / dt = 225 / (π 90^2) = 0.027 cm/min

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