When a circular plate is heated in an oven, its radius increases at the rate of 0.01 cm/min. At what rate is the plate's area increasing when the radius is 50cm? Be sure to include units in your answer.

3.14 cm²/min

Step-by-step explanation:

rate of increasing of radius, dr/dt = 0.01 cm/min

r = 50 cm

Area of plate, A = πr²

rate of increase of area

dA/dt = 2πr dr/dt

dA/dt = 2 x 3.14 x 50 x 0.01

dA/dt = 3.14 cm²/min

Thus, the increase of rate of area is 3.14 cm²/min.