When a circular plate of metal is heated in an oven its radius increases at a rate of 0.04cm per min At what rate is the plates area increasing when the radius is 42cm?

We note that the area of a circle is as follows: A = pir2.

Taking the derivative with respect to time:

dA/dt = 2pi * dr/dt

As r = 42cm and dr/dt = 0.04cm/min,

dA/dt = 2*pi*42cm*(1/25)cm/min

=84pi/25 cm2/min

= approx 10.556 cm2/min