Question

When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min. At what rate is the plate's area increasing when the radius is 60 cm? The rate of change of the area is□cm2/min. (Type an exact answer in terms of π.)

Answer 1

here ,

for the radius ,

dr/dt = 0.02 cm/min

r = 60 cm

for the area

rate of increase in area = dA/dt

rate of increase in area = d/dt(pi * r^2)

rate of increase in area = 2pi * r * dr/dt

rate of increase in area = 2pi * 60 * 0.02

rate of increase in area = 7.54 cm^2/min

the rate of increase in area is 7.54 cm²/min