Question

(b) 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 m/s, how fast is the area of the spill increasing when the radius is 26 m?

Answer 1

Explanation:

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Answer 2

Answer:

163.4 or $52\pi$ m2/s

Explanation:

The rate of change of the radius is 1 m/s

$\dfrac{dr}{dt}=1$

The area of a circle is

$A=\pi r^2$

We differentiate this to get the rate of change of the area with the radius:

$\dfrac{dA}{dr}=2\pi r$

The rate of change of the area is

$\dfrac{dA}{dt} = \dfrac{dA}{dr}\times\dfrac{dr}{dt}=2\pi r \times1 = 2\pi r$

At r = 26 m,

$\dfrac{dA}{dt}=2\pi \times26=52\pi=163.4$