Question

A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the instant the radius is 30 cm? A. 5/(36pi)cm/min

B. 2/(18pi)cm/min
C. 4/(9pi)cm/min
D. 7/(24pi)cm/min

Answer 1

The volume of the sphere is expressed in the formula V = 4/3 pi r^3. The rate of change of volume is determined by differentiating the formula: dV/dt = 4pi r^2 dr/dt. When we substitute 500 cm3/min as dV/dt and 30 cm as r. Then dr/dt is equal to 0.0442 cm/min