Question

A circular puddle of water is expanding in radius at a rate of 4.5 inches per second. At what rate is the Area expanding if the radius is 10 inches? 2.826 inches² per second 282.6 inches² per second 62.82 inches² per second 628.2 inches² per second

Answer 1

Answer: 282.6 inches²

Explanation: use the formula for the area of a circle, A = πr², where A is the area, π is 3.14159 and r is the radius of the circle;

d/dtA = πd/dtr * r² A = π * (10 + 2t)² d/dtA = π(10 + 2t) * 2 * 10 + 2π * (1 + 2t)² d/dtA = 282.6 inches² per second