Answer
a) $64 \pi cm^2/sec$
b) $256 \pi cm^2/sec$
Work Step by Step
The area of a circle is given by $A = \pi r^2$
If the radius is increasing at 4 cm/min, this means $\frac{dr}{dt} = 4$
To find the rate of change of the area, we have
$\frac{dA}{dt} = 2\pi r \frac{dr}{dt} $
a) when r = 8cm we have
$\frac{dA}{dt} = 2\pi (8)(4) = 64\pi cm^2/sec $
b) when r = 32cm we have
$\frac{dA}{dt} = 2\pi (32)(4) = 256\pi cm^2/sec $
