Question

An offshore rig begins to spill oil in a circular patch centered on the rig. If the radius ofthe oil spill increases at a rate of 30 m/hr, how fast is the area of the oil spill increasing when the radiusis 100 meters

Answer 1

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

Step-by-step explanation:

The area of a circle is given b

A=πr²

Then,

dA/dr= 2πr

Also give that,

dr/dt=30m/hr, r=100m

We want to find dA/dt

dA/dt=dA/dr×dr/dt

dA/dt= 2πr × 30

dA/dt= 2 ×π ×100×30

dA/dt=18849.56m²/s.

The rate of the area is 18849.56m²/s