A stone is dropped into a quiet lake and waves move in circles at a sp

1.	A stone is dropped into a quiet lake and waves move in circles at a speed of 3.5 cm per second. At the instant when the radius of the circular wave is 7.5 cm, how fast is the enclosed area increasing? (Take π = 22/7).
Answer» Consider the radius of circle as r dr/dt = 3.5 cm/s We know that area of circle = πr² So the rate of change of area of circle = 2πr dr/dt By substituting the values = 2 × 3.14 × 7.5 × 3.5 On further calculation = 165 cm²/s

A stone is dropped into a quiet lake and waves move in circles at a speed of 3.5 cm per second. At the instant when the radius of the circular wave is 7.5 cm, how fast is the enclosed area increasing? (Take π = 22/7).

Answer»

Consider the radius of circle as r

dr/dt = 3.5 cm/s

We know that area of circle = πr²

So the rate of change of area of circle = 2πr dr/dt

By substituting the values

= 2 × 3.14 × 7.5 × 3.5

On further calculation

= 165 cm²/s