A stone is dropped into a still pond sends out a circular ripple who’s radius increases at a constant rate of 2 m/sec. How rapidly is the area enclosed by the ripple increasing at the end of 20 sec?

1 Answer
Barry H.
Mar 6, 2018

#160pi# mtrs^2#/sec#.

Explanation:

Area of circle =#pir^2#....... #A=pir^2#......#[1]#

Differentiating ....#[1]# with respect to time, #[dA]/[dt]=2pir[dr]/[dt]#............#[2]#. If the radius is increasing at a constant rate of #[2m]/ [sec]# then after 20 seconds radius =#40 mtrs#.

We know #[dr]/[dt#= #[2mtrs]/[sec]# and so #[dA]/[dt]=[2]pi[40][2]#=#160pim^2#sec

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