The number of boxes fitted in the larger container is found out by the volume of both boxes.
The number of boxes fitted into the larger container is 480.
<h3>
What is the volume?</h3>
The volume can be defined as the space occupied by an object in three dimensions.
Given that the edge of the cube box is 1/4 ft. The dimensions of the larger box are 3 ft long, 1 1/4 ft wide, and 2 ft.
The volume of the cube box is calculated as given below.
![V_s = s^3](https://tex.z-dn.net/?f=V_s%20%3D%20s%5E3)
Where Vs is the volume of the cube box and s is the edge of the cube box.
![V_s = \dfrac {1}{4}^3](https://tex.z-dn.net/?f=V_s%20%3D%20%5Cdfrac%20%7B1%7D%7B4%7D%5E3)
![V_s = 0.015625\;\rm ft^3](https://tex.z-dn.net/?f=V_s%20%3D%200.015625%5C%3B%5Crm%20ft%5E3)
The volume of the larger box is calculated as given below.
<em />![V = l \times w\times h](https://tex.z-dn.net/?f=V%20%3D%20l%20%5Ctimes%20w%5Ctimes%20h)
Where V is the volume, l is length, w is width and h is the height of the larger box.
![V = 3 \times \dfrac {5}{4} \times 2](https://tex.z-dn.net/?f=V%20%3D%203%20%5Ctimes%20%5Cdfrac%20%7B5%7D%7B4%7D%20%5Ctimes%202)
![V = 7.5\;\rm ft^3](https://tex.z-dn.net/?f=V%20%3D%207.5%5C%3B%5Crm%20ft%5E3)
The number of cube boxes fitted into the larger box is calculated as given below.
![No. \; of \;boxes = \dfrac {V}{V_s}](https://tex.z-dn.net/?f=No.%20%5C%3B%20of%20%5C%3Bboxes%20%3D%20%5Cdfrac%20%7BV%7D%7BV_s%7D)
![No. \; of \;boxes = \dfrac {7.5}{0.015625}](https://tex.z-dn.net/?f=No.%20%5C%3B%20of%20%5C%3Bboxes%20%3D%20%5Cdfrac%20%7B7.5%7D%7B0.015625%7D)
![No. \; of \;boxes = 480](https://tex.z-dn.net/?f=No.%20%5C%3B%20of%20%5C%3Bboxes%20%3D%20480)
Hence we can conclude the number of boxes fitted into the larger container is 480.
To know more about the volume, follow the link given below.
brainly.com/question/1578538.