A spherical soap bubble has radius (in centimeters) seconds after formation given by…

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A spherical soap bubble has radius

r

(in centimeters)

t

seconds after formation given by

r(t)=\sqrt{0.04t}.

The bubble grows while the surrounding air remains at standard atmospheric pressure. (a) Calculate

\dfrac{dr}{dt}

as an explicit function of

t

. (b) Evaluate

\dfrac{dr}{dt}

t=25

and state the correct units. (c) Interpret the numerical result from part (b) in the physical context of the bubble’s growth.