Luke J. answered • 12/03/21

Experienced High School through College STEM Tutor

Given:

dA/dt = -17 in^{2} / s

r = 1 in

Find:

dC/dt = ? in / s @ r = 1 in

Solution:

C = 2πr ⇒ dC/dt = 2π dr/dt

A = πr^{2} ⇒ dA/dt = 2πr * dr/dt = 2π dr/dt * r

∴ dA/dt = dC/dt * r ⇒ dC/dt = 1/r * dA/dt = 1 / 1 ~~in~~ * ( - 17 in^{2} / s )

∴ __dC / dt = -17.000 in / s__

I hope this helps and that my derivation of finding the rate of change of circumference made sense! Message me in the comments for any questions, comments, or concerns!