Please help with this problem

Question

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2.5 m/s. How fast is the area of the spill increasing when the radius is 16 m?

Answer 1

Let A = area of the spill at time t and r = radius at time t.

Given dr/dt = 2.5. Find dA/dt when r = 16

A = πr²

dA/dt = 2πr(dr/dt) = 32π(2.5) = 80π m²/sec