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

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

zarkon · Answer

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

phi · Answer

can you post the first step you took?

anonymous · Answer

I just plugged in everythingto the area of a circle formula

phi · Answer

$$ A = \pi r^2 $$
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 ?

phi · Answer

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