Final answer:
Montgomery can fill 162 cubes with the sand from his box measuring 24 inches by 36 inches by 12 inches, by calculating the volume of the large box and dividing it by the volume of a 4 inch cube.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with volume calculation and the concept of division to find the number of smaller volumes that can fit into a larger volume. The student wants to know how many 4 inch cubes can be filled with sand from a larger box that measures 24 inches by 36 inches by 12 inches. To solve this, we first calculate the volume of the large box, which is length x width x height. The formula gives us a result of 24 in. × 36 in. × 12 in. = 10368 in.³. Then we calculate the volume of a 4 inch cube, which is 4 in. × 4 in. × 4 in. = 64 in.³. To find out how many of these cubes can be filled, we divide the volume of the large box by the volume of a single cube: 10368 in.³ ÷ 64 in.³ = 162. So, Montgomery can fill 162 cubes with the sand from the large box.