Question

A square is inscribed in a circle. How fast is the area of the square changing when the area of the circle is increasing at the rate of 1 in^2/min?

Answer 1

A circle = pi r^2
dA = + pi d (r^2) / dt
dA/dt = + pi 2r dr /dt
(dA/dt ) / 2pi r = dr / dt
r^2=2c^2
r^2/2=c^2 = A square
r dr /dt = dA square /dt
substitute dr
(dA/ dt) / 2pi = dA square / dt
where dA /dt is your rate of change of circle area