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 Question from Stephanie: My child had the question: A candy box has the following measurements. 10x6x4Find the total volume. (We got that one right 240in3) But... then it said “How many 1/2 inch cubed pieces of candy can fit in the box? This is where we disagree. Please help.

Hi Stephanie,

The volume of a box is the length times the width times the height which is how I think you found the volume to be

$10 \times 6 \times 4 = 240 \mbox{ cubic inches.}$

A half inch cube is 1/2 inch by 1/2 inch by 1/2 inch so its volume is

$\frac12 \times \frac12 \times \frac12 = \frac18 \mbox{ cubic inches.}$

Hence it takes 8 half inch cubes to fill 1 cubic inch and hence $8 \times 240$ half inch cubes to fill 240 cubic inches.

Penny