Question

a circular plate of metal is being heated in an oven. its radius is increasing at a rate of 0.017 inches/hour. at what rate is the plate's area increasing when its area is 1600π square inches?

Answer 1

A = pi. r2

Differentiate wrt time

Answer 2

Find r from the area A = pi r^2

Find circumference C = 2 pi r

For small fractional changes, the area will increase as (C) (dr/dt), where dr/dt is the rate at which the radius is increasing.

Answer 3

I'm sorry i am confused! ):

Answer 4

Simpler approach: Fine r from A = pi r^2.
After an hour r will be 0.017 in bigger.
Calculate the new area from A' = pi (r + 0.017)^2
Change in A per 1 hour is A' - A. That's the rate.