The volume of air in a balloon is represented by the function V (r) = four-thirds pi r cubed, where r is the radius of the ballo
on, in inches. The radius of the balloon increases with time, in seconds, by the function r (t) = one-fourth t squared. Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the two true statements.
Answer: You do not need calculus for this problem, as it is currently stated. Is something missing from the problem statement? If not, then just find the difference between the volumes. That will be the additional air required to inflate from the lower volume to the higher volume. For r in inches and V(r) in inches cubed,
V1(r) = (4/3)πr3
V2(2) = (4/3)π(r + 1)3
V2(r) - V1(r) = (4/3)π[(r + 1)3 - r3]
That is your function. You can simplify it further if you wish.
