The area of a circle is increasing at the rate of pi cm^(2)/min. At what rate is the radius increasing when the area is 4pi cm^(2)?
This problem deals the rate of change. For the formula of the area of a circle, we differentiate both sides with respect to time t. (A = πr^2) d/dt dA/dt = 2πr (dr/dt) Since we don't know yet the radius r, the area of a circle is given. A = πr^2 r^2 = A/π = 4π/π r^2 = 4 r = 2 cm Therefore, the rate of the radius is dA/dt = 2πr (dr/dt) dr/dt = (dA/dt)/(2πr) dr/dt = π/(2π*2) dr/dt = 0.25 cm/min Hope this helps.