Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 4 mi²/hr. How rapidly is the radius of the spill increasing when the area is 10 mi²?

Question

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 4 mi²/hr. How rapidly is the radius of the spill increasing when the area is 10 mi²?

Answer 1

A= πr². dA/dt = 2πrdr/dt. So 4mi²/hr = 2π√(10/π)dr/dt. Hence dr/dt= 2/√(10π)mi/hr. dr/dt= .357 mi/hr.