Question

A spherical balloon with radius r inches has volume defined by the function below. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 4 inches. (Give the answer in terms of π and r.)

Answer 1

v = 4/3*pi*r^3

derivating both sides with respect to t
dv/dt = 4*pi*r^2*dr/dt

when d = 1.7, r = 0.85, and dv/dt = 2:
2 = 4*pi*(0.85)^2*dr/dt

thus
dr/dt = 1/(2pi*(0.85)^2)
=1/(2*3.14*0.85^2)
=0.22