If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

Step-by-step solution

The volume V of a sphere of radius r is given by V = 4 3 r³ . Differentiating both sides with respect to time t , we get dV dt = 4 r² dr dt . It is given that the volume is increasing at a constant rate, so dV dt = k , where k is a positive constant. Substituting this into the derivative equation, k = 4 r² dr dt . Solving for the rate of change of the radius, dr dt = k 4 r² . Since 4 r² is the surface area S of the sphere, we have dr dt = k S . This implies that the rate at which the radius is increasing is inverse