All cubical boxes are blue, and the one cuboidal box is green. If the volume of the smallest cubical box is 1 cubic inch, what is the volume of the green box?

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Solution

Volume of smallest cubical box is 1 cubic inch.
Therefore,

$edge \times edge \times edge$ = 1
${edge}^{3}$ = 1
Thus, $edge$ = 1 inch, on taking the cube root.

Width of the green box = 1 + 1 = 2 inches

Also, we see from the top, the combined edge lengths of three small cubes will make the length (or rather depth, as we move into the screen) of the green box.

Therefore, length of the green box = 1 + 1 + 1 = 3 inches

Also, we observe that 6 small cube edges will make the height of the green box.

Therefore, height of the green box = 2 + 1 + 3 = 6 inches

Therefore,
Volume of the green box = length x width x height
= 3 x 2 x 6
= 36 cubic inches

Option a will be the correct answer.

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