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 1.5 m/s, how fast is the area of the spill increasing when the radius is 30 m?

The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.

Step-by-step explanation:

Derivative Rule:

Given that

The radius of the oil spill increases at a rate 1.5 m/s.

i.e

We need to find the rate of area increase i.e .

We know,

The area of the oil spills A =  ( since it spreads in circular pattern)

Differentiating with respect to t

Plug the value of

Plug r= 30 m

         =180 π m²/s

The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.