A company makes two sizes of boxes shaped like rectangle prisms. The large box is 16 inches tall 10 inches wide and 10 inches long. The drawing shows the mention of the small box. The small box is 4 inches tall 2 inches wide and 2 inches long.
Part A. what is the maximum number of small boxes that can fit in the larger box?
Part B. the company plans increase the width and length of the large box by 4 inches each to create a new larger box how many more of the small boxes will be able to fit inside this new larger box compared to the original large box
Part A:
To find the maximum number of small boxes that can fit in the larger box, we first need to calculate the volume of each box:
Large box volume = 16 x 10 x 10 = 1600 cubic inches
Small box volume = 4 x 2 x 2 = 16 cubic inches
Now, we divide the volume of the large box by the volume of the small box to find out how many small boxes can fit:
1600 / 16 = 100 small boxes
Therefore, the maximum number of small boxes that can fit in the larger box is 100.
Part B:
After increasing the width and length of the large box by 4 inches each, the new dimensions will be:
New large box dimensions = 16 x 14 x 14
Calculate the new volume of the large box:
New large box volume = 16 x 14 x 14 = 3136 cubic inches
Divide the new volume of the large box by the volume of the small box to find out how many small boxes can fit in the new larger box:
3136 / 16 = 196 small boxes
To find out how many more of the small boxes can fit in the new larger box compared to the original large box, we subtract:
196 - 100 = 96 more small boxes can fit in the new larger box compared to the original large box.