Helium is pumped into a spherical balloon at the constant rate of 25 cubic feet/minute. at what rate is the surface area of the balloon increasing at the moment when its radius is 8 feet?

If we let V', A', and r' represent the rates of change of the volume, area, and radius of the sphere, we can differentiate equations for V and A in terms of r, then eliminate r' to get an equation for A' in terms of V'.

Then, for the given values, the surface area is increasing at the rate ...

... A' = (2/8)·25 ft²/s = 6.25 ft²/s

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step-by-step explanation: