Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50 cm/s. Find the rate at which the area within the circle is increasing after 3 seconds

Answer 1

Take the total derivative of the area of a circle. \[A\text{=}\pi r^2\]\[\text{Dt}[A]= 2 \pi r \text{Dt}[r]\]Replace r with 150 and Dt[r] with 50.\[\text{Dt}[A]=2* \pi *150*50\]\[\text{Dt}[A]=15000 \pi\]\[\text{Dt}[A]=15000 \pi \text{ }\text{cm}^2\text{ per} \text{ second}\]

Answer 2

thanks!

Answer 3

I have the same problem but im getting 47,123 as the answer. What am i missing?

Answer 4

15000 Pi = 47123.9 to the nearest 1/10 th.