Question

cake batter poured into a pan creates a circular batter pattern whose radius increases at a constant rate of 1 in/sec. at what rate is the total batter area increasing at the end of 4 second

Answer 1

8 π .

Explanation:

radius increases at a constant rate of 1 in/sec.

dr / dt = 1

where r is radius .

radius after 4 sec

r = 1 x 4 = 4 in

area A = π r²

differentiating both sides

dA / dt = 2 π r dr / dt

Putting dr / dt = 1 , r = 4 in

dA / dt = 2 π x 4 x 1

= 8 π sq in per sec.

Area increases at the rate of 8 π per sec.