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 original volume of box

Volume of rectangular prism $V = l\times w\times h$. Original box has $l = 12$, $w = 18$, $h = 12$, so $V_{original}=12\times18\times12 = 2592$ cubic - inches.

Step2: Calculate volume of one cube

Volume of cube $v = s^{3}$, with $s = 6$, so $v=6\times6\times6 = 216$ cubic - inches.

Step3: Find new dimensions of box

Length and width of base are doubled. New length $l_{new}=2\times12 = 24$ inches, new width $w_{new}=2\times18 = 36$ inches, height remains $h = 12$ inches.

Step4: Calculate new volume of box

$V_{new}=l_{new}\times w_{new}\times h=24\times36\times12 = 10368$ cubic - inches.

Step5: Calculate number of cubes in new box

Number of cubes $n=\frac{V_{new}}{v}=\frac{10368}{216}=48$.

Answer:

C. 48