calculus
posted by Anonymous on .
The USPS will not mail a package if the sum of its length and its girth (measuring around the package) exceed 108 inches. Determine:
(a) The volume of the package as a function of its radius r.
(b) For which radius r is the volume of the package a maximum?
(c) What is the maximum volume of the package?

h = length
r = radius of cylinder package (I assume)
girth = 2 pi r
h + 2pi r = 108 for maximum
so h = (1082pir)
V = pi r^2 h
V = pi r^2 (1082 pi r)
dh/dr = pi r^2 (2pi) + (1082 pi r)2pi r
for max
2 pi r^2 = 216r  4 pi r^2
6 pi r^2 = 216 r
r = 216/(6 pi)
r = 11.5
then h = 108 2 pi r = 36
then V = pi r^2 h = 14851 in^3 
radius? Radius is on spheres. What kind of package are you askig about.

The question never specifies the shape of the package so it has really confused me on how to solve it.

Well by giving you r, it kind of implies a right circular cylinder.