Tyler’s family is using a shipping trailer that is 5 feet tall, 4 feet wide, and 12 feet long to load boxes of apples in. each box the apples are packed in has to have a volume of 5184 in3. design a box that will fill the trailer with no wasted space, and meet the volume requirements.

Tyler’s family is using a shipping trailer that is 5 feet tall, 4 feet wide, and 12 feet long.

Volume of the box = 5184 cubic inches

Total volume of trailer will be :

=> = 414720 cubic inches (1 feet = 12 inches)

Number of boxes that will fill this space =

= 80 boxes

We know the volume formula: L x W x H = 5184          

Here, L should divide into 12 (144 inches) evenly.

W should divide 4 (48 inches) evenly.

H should divide 5 (60 inches) evenly.

To solve for dimensions, lets suppose W= 24 inches

As L x W x H = 5184

So, L x H =

L x H = 216

Let us make H = 12 inches then we get L=18 inches

As stated above;

L=18 goes into 144 evenly by 8 times

H=12 goes into 60 evenly by 5 times

And W=24 goes into 48 evenly by 2 times  

And also boxes

So, these are one of the possible solutions to this question.