Question

A stone is thrown into a pond. A circular ripple is spreading over the pond in such a way that the radius is increasing at the rate of 6.4 feet per second. Find a function, r(t), for theradius in terms oft. Find a function, A(r), for the area of the ripple in terms of r. Find (A or) (t).

Answer 1

SOLUTION

From the question, the r is increasing at the rate of 6.4 feet per seconds.

This means that the equation of the radius is

$r=6.4\times t$

So the function for the radius, in terms of t becomes

$r(t)=6.4t$

The Area A is given as

$A=\pi r^2$

So, the function for the area in terms of r becomes

$A(r)=\pi r^2$

Now, (A . r)t becomes

$\begin{gathered} (A.r)t=\pi r^2,\text{ where r\lparen t\rparen = 6.4t, we have } \\ (A.r)t=\pi\times(6.4t)^2 \\ =40.96\pi t^2 \end{gathered}$

Hence the answer is

$(A.r)t=40.96\pi t^2$

The 3rd option is the answer