Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following.

Answer 1

@zepdrix

Answer 2

Your radius gets 40 cm longer after each second.\[r=x\times\frac{40cm}{s}\]

Answer 3

Lets say you wanted to find the radius after 2 seconds.\[r=2s\times\frac{40cm}{s}\]\[r=2\cancel{s}\times\frac{40cm}{\cancel{s}}\]\[r=2\times40cm\]\[r=80cm\]A circle with aradius of 80cm would have the area:\[A=\pi r^2\]\[A=3.14(80cm)^2\]\[A=20000cm^2\]