Abox 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

Hence, 48 cubes could be placed in the box.

Step-by-step explanation:

The dimension of a rectangular prism are given as:

12 inches by 18 inches by 12 inches.

Hence, the volume of the rectangular prism(V) is:

V=12×18×12 in^3.

Now the  length and width of the base are doubled.

Hence, the volume of the prism(V') is 4 times the volume of previous prism.

i.e. V'=4×V.

side of cube =6 inches.

Volume(v) of 1 cube=6×6×6 in^3.

Hence,

Let n cube could be placed in the box.

Hence,

n×v=V'

n×(6×6×6)=4V

n×216=4×(12×18×12)

Hence,

n×216=10368

n=10368/216

n=48.

Hence, 48 cubes could be placed in the box.

48

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