Question

A spherical balloon is inflated so that its volume is increasing at the rate of 2.9 cubic feet per minute. How rapidly is the diameter of the balloon increasing when the diameter is 1.4 feet?

Answer 1

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.