A spherical balloon is being inflated with air so that its radius increases at a…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A spherical balloon is being inflated with air so that its radius increases at a constant rate of 2 cm/s. The surface area S (in cm2) of a sphere with radius r centimeters is S=4πr2.
(a) Calculate the instantaneous rate of change of the surface area with respect to time when the radius is 10 cm. Express your answer with appropriate units.
(b) Determine whether the instantaneous rate of change of the surface area is increasing, decreasing, or remaining constant as the balloon continues to inflate. Support your conclusion with analytical reasoning or computation.