Mathematics

Problem

A spherical soap bubble has radius

r

(in centimeters). At a certain moment the radius is

3.0\text{ cm}

and is increasing at a rate of

0.020\text{ cm\,s}^{-1}

. The volume

V

of a sphere of radius

r

V=\dfrac{4}{3}\pi r^{3}

. (a) Calculate the rate at which the volume of the bubble is increasing, in cubic centimeters per second, at the instant described. (b) State the numerical answer from part (a) to three significant figures and interpret its physical meaning in the context of the expanding bubble.

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