Question

The area of a circular sun spot is growing at a rate of 1,500 km^2/s.

B) How fast is the radius growing at the instant when the sun spot has an area of 360,000 km^2? HINT [Use the area formula to determine the radius at that instant.] (Round your answer to four decimal places.)

Answer 1

So you know the area of circle is?

Answer 2

A=pi r^2

Answer 3

yep
and this clearly a rate problem
so we will need to find the derivative of that equation with respect to time.

Answer 4

pi2(r)(dr/dt)

Answer 5

and that is what dA/dt is equal to right?

Answer 6

yes

Answer 7

so we want to find dr/dt when the area=360000 km^2
and dA/dt=1500 km^2/s

Answer 8

do we plug it in A'?

Answer 9

yep but we still need to know what r is when A=360000

Answer 10

Recall A=pi*r^2
so what is r?

Answer 11

what is r when A=360000

Answer 12

.039

Answer 13

hmmm I'm not getting that as r

Answer 14

\[360000=\pi r^2 \]
can you solve this for r?

Answer 15

600/\[\sqrt{\pi}\]

Answer 16

that's good
so we have

that is r


ok and you got earlier that
\[A'=2 \pi r r' \]

Answer 17

So we have the A' and r
now we can find r'

Answer 18

replace A' with what it equals
replace r with what it equals

Answer 19

i don't know

Answer 20

then solve for r'

Answer 21

what does in those blanks?