Question

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. Help design a box that will fill the trailer with no wasted space, and meet the volume requirements.

Answer 1

Answer:

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 :

$5(12)\times4(12)\times12(12)$

=> $60\times48\times144$ = 414720 cubic inches (1 feet = 12 inches)

Number of boxes that will fill this space =

$414720/5184$ = 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 = $5184/24=216$

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 $8\times5\times2=80$ boxes

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

Answer 2

Hello.

To get the volume 5184 in3 you can use the dimension 18in x 24in x 12in.

First, you should draw a picture of your shipping container. It is a rectangular prism that is 5 by 12 by 4.

Next, let's look at the boxes of apples that will go into the box. The volume has to be 5184 in^3. If we divide it by 12 and 12, the answer is 3. Therefore, we could make a box that is 1 foot by 1 foot by 3 feet. 

Those boxes would be stack on the base without any left over space. Now, just figure out how many would go on the next rows. They would be able to stand up and down.

Have a nice day.