Answer:

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
