Question

A leak springs from an oil tanker in the ocean, spreading oil from the boat in a circle. If the oil patch gets 5 inches wider a minute, how quickly is the area of the oil spill increasing when the patch is 20 feet wide

Answer 1

600π in^2/min

Answer 2

150π in^2/min.

Explanation:

Area of circle A = πD^2/4

where D is the diameter of the circle.

now, taking differentiation w.r.t. to time t we get

dA/dt = π/4 ×2D×dD/dt

given dD/dt = 5in/min

therefore, dA/dt = π/4×2×5×(20×12)

=π/4×600

=150π in^2/min.