Given with the diameter, the volume of a sphere may be calculated through the equation, V = πD³ / 6 Differentiating both sides of the equation gives an answer of, dV/ dt = 3(π/6)D²(dD/dt) Substituting the known values, 2.9 ft³/min = 3(π/6)(1.4 ft)²(dD/dt) The value of dD/dt from the equation is 0.9419 ft/min. Thus, the diameter of the balloon is increasing at a rate of 0.9419 ft/min.
