Question

a spherical balloon is being inflated so that the radius is increasing at a rate of 3 cm/sec. find the rate at which the volume is increasing when r=10cm.

Answer 1

Answer:  1200pi cubic cm per sec

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Work Shown:

dr/dt = 3 is the rate of change of the radius

V = (4/3)pi*r^3 ..... volume of a sphere

dV/dt = (4/3)*3*pi*r^2*dr/dt ... chain rule

dV/dt = 4*pi*r^2*dr/dt

dV/dt = 4*pi*r^2*3

dV/dt = 12*pi*r^2

dV/dt = 12*pi*10^2 ... plug in r = 10

dV/dt = 1200pi