Question

he area of a circular sun spot is growing at a rate of 1,800 km2/s. How fast is the radius growing at the instant when it equals 5,000 km?

Answer 1

\[A=\pi r^2\]
Differentiating with respect to time, you have
\[\frac{dA}{dt}=2\pi r\frac{dr}{dt}\]
You're given that \(\dfrac{dA}{dt}=1800\) and you want to find \(\dfrac{dr}{dt}\) when \(r=5000\).

Answer 2

i keep on getting .115 km and im not exactly sure its corret

Answer 3

You should be getting
\[1800=2\pi(5000)\frac{dr}{dt}~~\iff~~\frac{dr}{dt}=\frac{1800}{10000\pi}=\frac{9}{50\pi}\]
What does that get you?

Answer 4

crap, i set it up incorrectly lol. thanks for the help :)

Answer 5

You're welcome!