Question

When a circular plate of metal is heated in an oven its radius increases at a rate of 0.01 cm/min. at what rate is the plates areas increasing when the radius is 54 cm?

Answer 1

3.3912cm³/min

Explanation:

Area of the circular plate = πr² where r is the radius of the plate.

dA/dt is the rate at which the plate is increasing

since dA/dr = 2πr and dr/dt = 0.01cm/min

dA/dt = dA/dr * dr/dt

dA/dt = 2πr dr/dt

dA/dt = 2π(54)(0.01)

dA/dt = 2π(0.54)

dA/dt = 3.3912cm³/min

Hence the rate at which the plates area is increasing when the radius is 54cm is 3.3912cm³/min