Math Problem. Please Help

Question

A pebble falls in a pond and the ripples spread out in a circular pattern. If one circular ripple

spreads out such that the radius grows by 3 feet/second, how fast is the circle’s area increasing

when the radius is 8 feet long? Leave your answer in terms of π .

Answer 1

Area = pi r^2 Take the derivative of both sides With respect to time

da/dft= 2pir dr/dt

you want to solve for da/dot which how fast the area is changing when r=8 and you are given dr/et=3

so da/dt= 2pi(8)(3) = 48pi ft/second