Answer :
The rate of change of Area of the circle of ripples when radius is 24 inches is 602.88 in²/sec .
In the question ,
it is given that ,
a rock dropped in pond causes a circular waves of ripples ,
the rate at which the radius is increasing (dr/dt) = 4 in/sec .
let the radius of the circular ripples is = r ,
the area of the circular ripples is ; A = πr² ,
differentiating Area with respect to time(t) is ,
dA/dt = π×2r×(dr/dt)
to find the rate of change of area when the radius of circle is 24 inches ;
substituting dr/dt = 4 and r = 24 ,
we get ,
dA/dt = π×2×24×4
= 192×3.14 .
= 602.88 in²/sec
Therefore , the rate of change of Area is = 602.88 in²/sec .
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