A stone is dropped in a quiet lake. If the produced circular waves increase at a rate of 4 cm/sec, then find the rate of increase in its area when the redius of circular wave is 7 cm.

Options

A. `172 cm^(2)`/sec
B. `174 cm^(2)`/sec
C. `178 cm^(2)`/sec
D. `176 cm^(2)`/sec

Answer

D

Explanation

Let at any time 't' the radius of circular wave be 'r' and its area be 'A'.
Given that `(dr)/(dt) = 4` cm/sec.
Now A = `pi r^(2)`
`rArr (dA)/(dt)=pi.d/(dt)(r)^(2)=pi. 2r. (dr)/(dt)`
At `r = 7 cm` ,
`(dA)/(dt)=(22)/7xx2xx7xx4 = 176 cm^(2)`/sec
Therefore the area of circular wave will increase at a rate of `176 cm^(2)//sec`.