# Chapter 2 - Differentiation - 2.6 Exercises: 11

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 $\frac{dA}{dt} = 2\pi (32)(4) = 256\pi cm^2/sec$

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