I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
The question is:
The area of a circular sunspot is growing at a rate of 600 km ^ 2 / sec.
b. How fast is the radius growing at the instant when the sunspot has a area of 640,000 km ^ 2? (Round your answer to 4 decimal places).
For this case the first thing we should know is that by definition the area of the circle is given by:
A = pi * R ^ 2
Where,
R: radio
We must first determine the radius:
R = (A / π) ^ 0.5
R = (640000 / π) ^ 0.5 km
Then, we derive the equation:
A '= pi * (2RR')
We cleared R '
R '= (A') / (2 * π * R)
Substituting values:
R '= (600) / (2π (640000 / π) ^ 0.5)
R '= 0.2116 km / sec
Answer:
the radius is growing at:
R '= 0.2116 km / sec
