Question

Calculas 1 help I get pi/3 for answer

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6mi^2/h How fast is the radius of the spill increasing when the area 9 mi^2

my book says the answer is 1/sqrt(pi) mi/h

Answer 1

your book is correct....what did you do?

Answer 2

can you post the first step you took?

Answer 3

I just plugged in everythingto the area of a circle formula

Answer 4

\[ A = \pi r^2 \]
there is no "change in area" nor "change in radius"
you must take the derivative (with respect to time "t") of both sides. Do you know how to do that ?

Answer 5

if you take the derivative of r^2 with respect to t, you should get
\[ \frac{d}{dt} r^2 = 2 r \frac{d}{dt} r = 2r \frac{dr}{dt}\\ = 2\ r \ \dot{r}\]