Question

(b) how fast is the radius growing at the instant when the sunspot has an area of 640,000 square kilometers? hint [use the area formula to determine the radius at that instant.] (round your answer to four decimal places.) 4.331 incorrect: your answer is incorrect. km/s

Answer 1

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