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

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

163.4 or
`52\pi` m2/s

Step-by-step explanation:

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

`(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:

`(dA)/(dr)=2\pi r`

The rate of change of the area is

`(dA)/(dt) = (dA)/(dr)*(dr)/(dt)=2\pi r *1 = 2\pi r`

At r = 26 m,

`(dA)/(dt)=2\pi *26=52\pi=163.4`