The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu
s of the sphere is 3m?
1 answer:
The balloon has a volume
dependent on its radius
:

Differentiating with respect to time
gives

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

The surface area of the balloon is

and differentiating gives

so that at the moment the radius is 3 m, its area is increasing at a rate of

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