The Post Office used to have a strange way of limiting the size of packages. The maximum allowed was a 2 meters combined length and girth. Given this restriction, what is the greatest volume of a package that is shaped like a rectangular prism with whole centimeter dimensions? (Remember that 100 cm = 1 m)

Step-by-step explanation:

we know that

The maximum volume for a rectangular prism is when the base is a square

The girth is the distance around the package perpendicular to the length

see the attached figure to better understand the problem

Let

x ----> the length of the square base of the prism

h ---> the height of the prim

we have that

-----> equation A

The volume of a rectangular prism is given by

where

B is the area of the base

h is the height of the prism

we have

so

----> equation B

substitute equation A in equation B

Find the first derivative of the function

equate to zero

---->

therefore

The greatest volume  is equal to