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

Answer:

$1\frac{1}{7} yards$

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:

$H = \frac{V}{L * W}$

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:

$H = \frac{10}{2\frac{1}{2} * 3\frac{1}{2} } \\\\H = \frac{10}{\frac{5}{2} * \frac{7}{2} }$

$H = \frac{10}{\frac{35}{4} } \\\\H = \frac{10 * 4}{35} \\\\H = \frac{40}{35} = \frac{8}{7} = 1\frac{1}{7}$

The maximum height of the container is $1\frac{1}{7} yards$.