water spreads in a circle whose area increases at a constant rate of 5.5 mi2/hr. How rapidly is radius of the spill increasing when the area is 9 mi2?

Question

related rates word problems

Answer 1

A = πr² ⇒

 

dA/dt = 2πr dr/dt ⇒

 

dr/dt = (dA/dt) / (2πr)

 

r = √(A/π)

 

dr/dt = dA/dt / [2π√(A/π)]

 

Plug in the following:

 

dA/dt = 5.5 mi²/hr

A = 9 mi²,

 

and get dr/dt.  You can finish from here.