Question

a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.
if the length and width of the base are doubled, how many cubes could the new box hold?
○ 18
○ 24
○ 48
○ 96

Explanation:

Step1: Calculate the number of cubes along each dimension for the original box

• For length: \(12\div6 = 2\)
• For width: \(18\div6=3\)
• For height: \(12\div6 = 2\)
• Number of cubes in original box: \(2\times3\times2=12\) (This step is just to show the logic, we can also use the ratio method directly)

Step2: Calculate the new dimensions after doubling length and width

• New length: \(12\times2 = 24\) inches, number of cubes along new length: \(24\div6=4\)
• New width: \(18\times 2=36\) inches, number of cubes along new width: \(36\div6 = 6\)
• Height remains \(12\) inches, number of cubes along height: \(12\div6=2\)

Step3: Calculate the number of cubes in the new box

• Number of cubes \(=4\times6\times2\)

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Answer:

C. 48