Answer:
a) The greatest number of small toy boxes that can be packed is 1512.
b) The volume of the large box is 189 in³.
Step-by-step explanation:
a) We analyze the quantity of smaller boxes that fit in each side:
Width: 12 in ÷ 1/2 in= 24
Length: 4 1/2 in ÷ 1/2 in= 9
Height: 3 1/2 in ÷ 1/2 in= 7
So if we multiply each number we can get the quantity of small boxes:
24×9×7=1512 small boxes
b) The volume of the small box is:
V=(1/2 in)³=1/8 in³
Now, we multiply the volume of the small box by the total quantity of small boxes:
Total volume=1/8 in³×1512=189in³