Answer:
[tex]1\frac{1}{7} yards[/tex]
Step-by-step explanation:
The maximum volume the shipping container can have is 10 cubic yards.
The volume of a rectangular prism is given as:
V = L * W * H
where L is length, W is width and H is height.
To find the maximum height of the container, make H the subject of formula:
[tex]H = \frac{V}{L * W}[/tex]
We have been given the length and width of the container as 2 1/2 yards and 3 1/2 yards respectively.
Hence, the maximum height is:
[tex]H = \frac{10}{2\frac{1}{2} * 3\frac{1}{2} } \\\\H = \frac{10}{\frac{5}{2} * \frac{7}{2} }[/tex]
[tex]H = \frac{10}{\frac{35}{4} } \\\\H = \frac{10 * 4}{35} \\\\H = \frac{40}{35} = \frac{8}{7} = 1\frac{1}{7}[/tex]
The maximum height of the container is [tex]1\frac{1}{7} yards[/tex].
