A circle is inside a square.
The radius of the circle is decreasing at a rate of 4 meters per day and the sides of the square are increasing at a rate of 2 meters per day.
When the radius is 3 meters, and the sides are 19 meters, then how fast is the AREA outside the circle but inside the square changing?
The rate of change of the area enclosed between the circle and the square is *blank*
square meters per day.
square: side s, area=s^2
circle: radius r, area=πr^2
so we want the difference between the areas:
a = s^2 - πr^2
da/dt = 2s ds/dt - 2πr dr/dt
at the moment in question,
da/dt = 2(19)(2) - 2π(3)(-4) = 76+24π m^2/day
let the side of the square be x m
let the radius of the circle be r m
A = area between square and circle
= x^2 - πr^2
dA/dt = 2x dx/dt - 2πr dr/dt
= 2(19)(2) - 2π(3)(-4)
= ...
etc