When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min.

Question

This is the rest of the question... At what rate is the plate's area increasing when the radius is 53 cm?

 

I have to answer in the following format.. The rate of change of the area is [] cm^2/min

 

 

Answer 1

Let r = radius (in cm) at time t min

     A = area (in cm²) at time t min

 

A = πr²

 

GIVEN:  dr/dt = 0.02 cm/min

 

FIND:  dA/dt when r = 53 cm

 

Differentiate the area formula with respect to t:

 

 dA/dt = π(2r)(dr/dt)

 

         = π(2(53 cm))(0.02 cm/min)

 

         = 2.12π cm²/min

 

         ≈ 6.66 cm²/min