Calculus

A spherical balloon is inflated at a rate of 10 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 4 feet?

And

The radius of a circle is decreasing at a rate of 2 ft/minute. Find the rate at which the area is decreasing with respect to time when the radius is 4 feet?

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  1. V = (4/3)πr^3
    dV/dt = 4πr^2 dr/dt
    given dV/dt = 10 ft^3/min
    so at r = 4
    10 = 4π(16) dr/dt
    dr/dt = 10/(64π) or appr. .05 ft/min

    If A = 4πr^2, do the second question the same way.

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