Posted by **Anonymous** on Saturday, March 19, 2011 at 7:50pm.

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

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

- 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.

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