A circular plate of metal expands by heat so that it’s radius increases uniformly at the rate of .01 inch per second. At what rate is the surface increasing when the radius is two inches?

Question

Thank you for the help!

Answer 1

The surface area of an expanding plate is calculated (at any moment in time) as:

A = π•r²

The rate of expansion (dA/dt) can be calculated by taking the derivative of this equation with respect to time:

(through the use of the chain rule)

So dA/dt = 2π(2)(.01) ≈ 0.126 in²/s