Question

A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 5 feet per minute. Find the rate at which the area is changing at the instant the radius is 12 feet.

Answer 1

Answer:

376.9911ft²/minute

Explanation:

In the given question the rate of chage of radius in given as

$\frac{\mathrm{d}r }{\mathrm{d} t}$=5ft per minute

we know ares of circle A=pi r^{2}

differentiating w.r.t. t we get

$\frac{\mathrm{d} A}{\mathrm{d} t}=2\pi r\frac{\mathrm{d}r }{\mathrm{d} t}$

Now, we have find $\frac{\mathrm{d}A }{\mathrm{d} t} at r=12 feet$

$\frac{\mathrm{d} A}{\mathrm{d} t}=2\times\pi\times12\times5=120\pi=376.9911ft^{2}/minute$