Question

) The diameter of a circle is increasing at a rate of 5 cm/sec. How fast is the area changing with time when the diameter is 20 cm

Answer 1

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