The temperature (in ) of a solid metal ball is modeled by

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The temperature (in

^{\circ}\text{C}

) of a solid metal ball is modeled by

T=5r^2

, where

r

is the ball’s radius in centimeters. When

r=3\text{ cm}

the radius is decreasing at

\dfrac{dr}{dt}=-0.02\text{ cm/s}

. Calculate

\dfrac{dT}{dt}

at that instant, including units.