A spherical iron ball cools as it solidifies

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

A spherical iron ball cools as it solidifies. Its radius

r

(in centimeters) is decreasing at a constant rate of

0.02\text{ cm}/\text{s}

. The temperature

T

(in Kelvin) of the ball is related to its radius by the model

T(r)=300+\frac{50}{r}.

Assume all functions are differentiable. (a) Calculate

\dfrac{dT}{dt}

, the instantaneous rate of change of temperature with respect to time, at the moment the radius is

5\text{ cm}

. Include correct units in your answer. (b) Interpret the sign and magnitude of the value you found in part (a) in the context of the cooling ball.