A crowd gathers around a movie star, forming a circle.

Question

The radius of the crowd increases at a rate of 6 ft/sec. How fast is the area taken up by the crowd increasing when the radius is 14 ft?    Related Rates of AP Calculus!!!! Please help!!!!

Answer 1

Hi Gabriele,

 

This is mathematically exactly the same as the last problem I did for you with the circular puddle of water on the floor. Follow those steps exactly, but let r = 14 ft and dr/dt = 6 ft/sec and solve for dA/dt.

Answer 2

A = area of circle r = radius t = time

 

A = πr^{2  , r =14}

dr/dt= 6 ( given)

 

dA/dt= 2πrdr/dt= 12Πr= 192Π