#45 ASAP What is the rate of change, in square inches per second

Question

A region is bounded by two concentric circles, as shown by the shaded region in the figure above. The radius of the outer circle R  is increasing at a constant rate of 2 inches per second. The radius of the inner circle,r, is decreasing at a constant rate of 1 inch per second. What is the rate of change, in square inches per second, of the area of the region at the instant when r is 4 inches and r is 3 inches?

3pi

6pi

10pi

22pi

Answer 1

Area A = π(R² - r²);

dA/dt = 2π(RdR/dt - rdr/dt) = 2π(4·2 - 3(- 1))= 22π in²/s