The area of a circle is decreasing at rate of 5m^2/s when its radius is 3m. At what rate is the radius of the circle decreasing at that moment? At what rate is the diameter decreasing at that moment?

Answer 1

Area, A = πr² where r = the radius of the circle

A' = 2πrr' --> r' = A'/(2πr)

a)

r'(3) = 5/(2π(3)) = 5/(6π) m/s

b) let d = the diameter

d = 2r

d' = 2r'

d'(3) = 2r' = 5/(3π) m/s