Mathematics

Problem

(Circle and its expanding area) A circle is expanding as time passes. (i) State the mathematical relation between the area

A

of the circle and its radius

r

. (ii) Differentiate your relation with respect to time

t

to obtain an explicit expression connecting

\dfrac{dA}{dt}

and

\dfrac{dr}{dt}

. (iii) Clearly explain why the units of

\dfrac{dA}{dt}

are always the square of the units of

\dfrac{dr}{dt}

per unit time.