A spherical balloon is inflated with gas at a rate of 700 cubic centimeters per minute. (a) Find the rates of change of the radius when r = 50 centimeters and r = 75 centimeters. r = 50 cm/min r = 75 cm/min (b) Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant. dr depends on r, not simply r. dt O The rate of change of the radius is a linear relationship whose slope is dv dt O The volume only appears constant; it is actually a rational relationship. The rate of change of the radius is a cubic relationship. as a function runs parallel to the volume function, which is not linear. dt

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