Aspherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute. (a) find the rates of change of the radius when r = 70 centimeters and r = 95 centimeters. r = 70 cm/min r = 95 cm/min. (b) explain why the rate of change of the radius of the sphere is not constant even though dv/dt is constant. the rate of change of the radius is a linear relationship whose slope is dv dt . the volume only appears constant; it is actually a rational relationship. dr dt as a function runs parallel to the volume function, which is not linear. the rate of change of the radius is a cubic relationship. dr dt depends on r2, not simply r.