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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

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Manetho

Answer:

150π in^2/min.

Step-by-step 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.

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