How many wooden toy cubes with a 3 inch edge can fit in a rectangular container with dimensions 3 inches by 21 inches by 15 inches?

Answer 1

The first thought is to find the volume of the container, the volume of one of the cubes and divide them to find out how many cubes can be fitted in. However, unless the dimensions are exact multiples of the cubes this can give a higher result than can actually be placed in the container as the space left over will require the cubes to be cut up.

In this case the dimension are exact multiples of the cube, so it will work:

Volume = length × width × height

volume_container = 3 in × 21 in × 15 in = 945 in³

volume_cube = 3 in × 3 in × 3 in = 27 in³

→ number of cubes that can be fitted = volume_container ÷ volume_cube

= 945 in³ ÷ 27 in³ = 35 cubes.

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The correct method is to see how many objects you can fit in a layer and how many layers can be fitted into the container:

• Divide the corresponding height measurements to get how many layers there are;
• Divide to corresponding width measurements to get how many in each row of each layer;
• Divide to corresponding length measurements to get how many in rows in each layer

Note that when dividing, any fractional part must be ignored - only the whole number part is used.

The cubes are 3 in (height) by 3 in (length) by 3 in (width).

The container is 3 in (height) by 21 in (length) by 15 in (width).

Dividing the heights gives: 3 in ÷ 3 in = 1 layer

Dividing the widths gives: 15 in ÷ 3 in = 5 cubes per row (per layer)

Dividing the lengths gives: 21 in ÷ 3 in = 7 rows per layer

So there is 1 layer which contains 7 rows each row containing 5 cubes

→ 1 × 7 × 5 = 35 cubes can be stored in the container.