Astone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50 cm/s. find the rate at which the area within the circle is increasing after 3 seconds

We are given the rate of change of radius of the circle.
dr/dt = 50 cm/s
Area of circle = πr²
dA/dr = 2πr
dA/dt = dA/dr x dr/dt
= 2πr x 50
= 100πr
Assuming the radius is 0 at time 0, after 3 seconds, the radius:
50 x 3 = 150 cm
Area increase rate:
100 x 150 x π
= 47,123.9 cm²/s