Question

A shipping container shaped like a rectangular prism must have a maximum volume of 10 cubic yards. If the container is 2 1/2 yards long and 3 1/2 yards wide, what is the maximum height of the container?

Answer 1

`1(1)/(7) yards`

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:

`H = (V)/(L * W)`

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:

`H = (10)/(2(1)/(2) * 3(1)/(2) ) \\\\H = (10)/((5)/(2) * (7)/(2) )`

`H = (10)/((35)/(4) ) \\\\H = (10 * 4)/(35) \\\\H = (40)/(35) = (8)/(7) = 1(1)/(7)`

The maximum height of the container is
`1(1)/(7) yards`.