Question

The radius of a circular puddle is growing at a rate of 5 cm/s.

Answer 1

How fast the radius is growing when at 1cm = 0.795774

Explanation:

At 1cm

dr/dx . is equal to 5cm^3/s

To find area: A=pir^2 --> A=pi(1)^2 --> A= 3.1415926

To find da/dt: da/dt= (2)(pi)(r)(dr/dt) --> da/dt=(2)(pi)(1)(5) = 31.41592654

To find how fast the radius is growing: 5/2pi = 0.795774

You can do the same steps with different radius's, just replace the 1's with whatever you are given (whether it be 10, 100, 1000, etc)

Answer 2

dr/dx = 5 is what can be used to represent that if that is what you want to know