Answer:
The maximum number of small boxes that can fit inside the large box are 100.
Step-by-step explanation:
There are some data missing in the question. The dimension of small box is not given so below is figure attached of the small box dimension.
Given:
A company makes two sizes of boxes shaped like rectangular prisms.
The Large box is 16 inches tall, 10 inches wide and 10 inches long.
Now, to find the maximum number of small boxes that can fit inside the large box.
So, we find the volume of large box first by putting formula:
Width = 10 inches.
Height = 16 inches.
Length = 10 inches.
[tex]Volume=width\times height\times length[/tex]
[tex]Volume=10\times 16\times 10[/tex]
[tex]Volume=1600\ cubic\ inches.[/tex]
Volume of large box = 1600 cubic inches.
Now, to find the volume of small box by using formula:
Width = 2 inches.
Height = 4 inches.
Length = 2 inches.
[tex]Volume=width\times height\times length[/tex]
[tex]Volume=2\times 4\times 2[/tex]
[tex]Volume=16\ cubic\ inches.[/tex]
Volume of small box = 16 cubic inches.
Now, to get the number of boxes that can fit inside the large box we divide volume of large box by volume of small box:
[tex]Number\ of\ boxes=\frac{Volume\ of\ large\ box}{Volume\ of\ small\ box}[/tex]
[tex]Number\ of\ boxes=\frac{1600}{16}[/tex]
[tex]Number\ of\ boxes=100.[/tex]
Therefore, the maximum number of small boxes that can fit inside the large box are 100.
