The radius of a heated circular metal disc varies with time according to the…

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The radius

r\,(\text{in mm})

of a heated circular metal disc varies with time

t\,(\text{in s})

according to the differential equation

\dfrac{dr}{dt}=0.02t^{2}

. Initially, at

t=0

, the radius is

50\,\text{mm}

. (i) Integrate the given differential equation to obtain an explicit expression for

r

as a function of

t

. (ii) Using this result, derive an expression for the rate of change of the disc’s area

A

with respect to time

t

. (iii) Calculate

\dfrac{dA}{dt}

when

t=5\,\text{s}

, giving your answer correct to the nearest whole number and specifying appropriate units.