KJSEA 2025 Maths Q22 — Volume of a Cube & Packing Small Cubes
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The Question
“A metallic container is in the shape of a cube, and each side of the container measures 2.4 metres. Part A asks you to find the volume of the container. Part B asks how many small cubes, each with a side of 50 centimetres, can be packed inside the container.”
Find the volume of the container
The container is a cube, so every side is the same length. The volume of a cube is found by multiplying the side by itself three times, which we write as the side cubed. Here the side is 2.4 metres, so multiply 2.4 by 2.4 by 2.4 to get the volume in cubic metres.
Put both cubes in the same units
The big container is measured in metres but the small cubes are measured in centimetres. Before comparing sizes we must use one unit. Since 100 centimetres make 1 metre, a small cube of side 50 centimetres is the same as 0.5 metres. Working in metres keeps everything consistent with Part A.
See how many small cubes fit along one edge
Line the small cubes up along one edge of the container. Divide the container's edge length by the small cube's side to see how many fit. The answer is 4.8, but you cannot pack part of a cube. Only four whole cubes fit along the edge, and a little empty space is left over.
Always round DOWN when packing whole objects, never up, because a partial cube cannot fit in the leftover gap.
Count the cubes in all three directions
The container is a cube, so the same thing happens along the length, the width, and the height: four small cubes fit each way. To find the total number that pack inside, multiply the count along each of the three directions together.
Final Result
The volume of the container is 13.824 cubic metres, and 64 small cubes (each of side 50 cm) can be packed inside it.
Why this method works
Multiplying the side three times works because a cube fills space in three directions at once — length, width and height — and each direction has the same length. For the packing part, we round the 4.8 down to 4 because a cube either fits whole or not at all; the leftover 0.8 of a cube's width is just empty space against the wall. Counting four cubes in each of the three directions and multiplying gives the full three-dimensional grid of cubes that actually fit, which is why the answer is 4 times 4 times 4.
Four cubes of 0.5 m span 2.0 m, leaving 0.4 m of empty space along each 2.4 m edge — not enough for a fifth cube, confirming that only 4 fit per edge and 64 in total.