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?
calculus - Damon, Saturday, March 19, 2011 at 8:09pm
h = length
r = radius of cylinder package (I assume)
girth = 2 pi r
h + 2pi r = 108 for maximum
so h = (108-2pir)
V = pi r^2 h
V = pi r^2 (108-2 pi r)
dh/dr = pi r^2 (-2pi) + (108-2 pi r)2pi r
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
calculus - bobpursley, Saturday, March 19, 2011 at 8:09pm
radius? Radius is on spheres. What kind of package are you askig about.
calculus - Anonymous, Saturday, March 19, 2011 at 8:16pm
The question never specifies the shape of the package so it has really confused me on how to solve it.
calculus - Damon, Saturday, March 19, 2011 at 8:18pm
Well by giving you r, it kind of implies a right circular cylinder.