Mathematics

Problem

The temperature of a spherical metal pellet is given by

T(r)=\dfrac{500}{1+0.1r^{3}}

(°C), where

r

is the pellet’s radius in centimeters and

r

varies with time

t

. Derive a simplified formula for

\dfrac{dT}{dt}

in terms of

r

and

\dfrac{dr}{dt}