Answer:
50π cm²/s
Step-by-step explanation:
Area of the circle A = πd²/4
Rate at which the area is changing with time is expressed as;
dA/dt = dA/dd*dd/dt
dd/dt is the rate at which the diameter is changing with time
dd/dt = 5cm/sec
dA/dd = 2πd/4
dA/dd = πd/2
Given that d = 20cm
dA/dt = dA/dd*dd/dt
dA/dt = πd/2*5
dA/dt = 20π/2 *5
dA/dd = 10π * 5
dA/dd = 50π cm²/s
Hence the area is changing at the rate of 50π cm²/s
