If by dropping a stone in a quiet lake a wave moves in a circle at a speed of , then the rate of increase of the enclosed region when the radius of the circular wave is , is
Step 1: Given Data
Step 2: Formula Used
The area() of the circular wave in terms of the radius() is,
When a stone is dropped into a lake, waves move in a circle of the speed() of , i.e. Radius of the circle increases at a rate of ,
is the time taken.
The rate of increase in the area concerning time is
Step 3: Calculate the rate of increasing area
The radius of the circle increases at a rate of ,
We know, that the area () of the circular wave in terms of the radius () is,
Now,
we know,=
When
Therefore, Area is increasing at the rate when .
Hence, option A is the correct option.