Question

Gr12 Calculus question, please help.

Answer 1

A circular oil spill on the surface of the ocean spreads outward. Find the approximate rate of change in the area of the oil slick with respect to its radius when the radius is 100 m.

Answer 2

so we need to know the area of circle formula thingy

Answer 3

A=2pir?

Answer 4

\[A=\pi r^2 \]

Answer 5

now do you know how to differentiate both sides w.r.t to the variable t.
t represents time.

Answer 6

no, sorry i forgot how to do that :( do we use limits?

Answer 7

pi is a constant multiple

so you have
\[\frac{dA}{dt}=\pi \frac{dr^2}{dt}\]

Answer 8

to find the derivative of r^2 use chain rule power rule combination

Answer 9

And i would find my answer after that or would there be a next step? :(

Answer 10

your goal is to find approximate A' when r=100

Answer 11

The answer on my book says 200pir^2 m^2/m

Answer 12

How would i find the units when I'm only given m?

Answer 13

that r in the answer makes no sense to me

Answer 14

did you mean 200 pi*m^2/m ?

Answer 15

Oh yes, no r. Sorry!

Answer 16

I will talk about the units
but first can you tell the derivative of r^2?

Answer 17

Ok I guess I will explain the units since you don't need help with the other part.
Area is measured with a square unit
Length is measured with a non square unit

So if your length is measured in m
Then your area is measured in m^2

A- > m^2
r-> m

and you have to find dA/dr so therefure your units is m^2/m

Answer 18

\[A(r)=\pi r^2 \\ \frac{dA}{dr}= \pi \frac{d(r)^2}{dr}=?\]