Asked by Darylynn
a stone is thrown into a pond creating ripples that are concentric circles. the rate of change of the radius of the circle is 3 ft/min. if the radius is 0 at the time=0, how fast is the area increasing after 4 minutes
Answers
Answered by
Arora
Radius = r
Area = 4π(r^2)
As per the question: dr/dt = 3ft/min
dr/dt = 3
When t = 4, r = t*3 = 4*3 = 12 ft
d(Area)/dt = d(4π*r^2)/dt
= 4π*2r*(dr/dt)
Plug in r = 12, dr/dt = 3, you'll get the answer (in feet squared per minute)
Area = 4π(r^2)
As per the question: dr/dt = 3ft/min
dr/dt = 3
When t = 4, r = t*3 = 4*3 = 12 ft
d(Area)/dt = d(4π*r^2)/dt
= 4π*2r*(dr/dt)
Plug in r = 12, dr/dt = 3, you'll get the answer (in feet squared per minute)
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