Related Rates: If the radius of the oil spill increases at

[tenshineko]

we just started learning this today, and i haven't really grasped what it is that we're doing... but this problem was assigned as part of our homework and i was hoping someone could help me understand how to do it...

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 1m/s, how fast is the area of the spill increasing when the radius is 30m? (its an even problem, so im not sure what the answer should come out to)

any help would be greatly appreciated

thank you

 

[galactus]

This is probably at the beginning of the homework on related rates. #2?.

Anyway, use the area of a circle formula: \(\displaystyle {\pi}r^{2}\)

Differentiate with respect to time:

\(\displaystyle 2{\pi}r\frac{dr}{dt}\)

Now, you have r and dr/dt. Enter them in and you have it.

 

[tenshineko]

thank you

 

[tenshineko]

and yes, it was #2