Unit 7 · Topic 04 · Geometry
Kabir's toy box was a perfect cube. Anaya's was a long, low cuboid.
Both held exactly the same number of 1 cm blocks — 216 of them.
Same amount of space inside, two completely different shapes.
Ms. Rao brought two boxes to class: a cube 6 cm on every side, and a cuboid 12 cm long, 6 cm wide and 3 cm tall. "Which one holds more?" she asked.
Kabir looked at the cube. "It looks smaller. It's shorter."
"Let's not guess — let's fill them with 1 cm blocks and count," said Ms. Rao.
For the cube, Anaya worked out how many blocks fit along each edge: 6 along the length, 6 along the width, 6 along the height. "If I lay one layer flat, that's 6 times 6, thirty-six blocks. And there are 6 layers stacked up, so 36 times 6 is 216 blocks."
For the cuboid, Kabir did the same: 12 along the length, 6 along the width, 3 layers tall. "One layer is 12 times 6, seventy-two blocks. Three layers is 72 times 3, which is 216."
"216 and 216," said Ms. Rao. "Exactly equal, even though one box is tall and square and the other is long and flat. That count of unit cubes — how much space a solid object takes up — is its VOLUME. And you've just discovered the formula yourselves: volume equals length times width times height."
"So it's like area, but stacked up?" asked Kabir.
"Precisely. Area covers a flat surface with square units. Volume fills a solid space with CUBE units — cubic centimetres, cubic metres. One more dimension, one more multiplication."
Anaya noticed something about the cube specifically. "Since a cube has all three sides equal, the formula is just side times side times side."
"Right — same shortcut as a square's area, one power higher," said Ms. Rao. She then posed one more: a fish tank 40 cm long, 20 cm wide, 25 cm tall. "How many cubic centimetres of water to fill it completely?"
Kabir multiplied: 40 × 20 = 800, then 800 × 25 = 20,000 cubic centimetres. "That's a lot of blocks."
"It is — and it's also exactly how much water the tank holds, since 1 cubic centimetre of water takes up exactly 1 cubic centimetre of space," said Ms. Rao.
Volume is the amount of space a solid object takes up, measured by counting how many unit cubes fit inside it — the units are CUBIC units (cubic cm, cubic m), one dimension more than area's square units.
For a cuboid (a rectangular box shape): volume = length × width × height.
For a cube (all three sides equal): volume = side × side × side.
Two very differently-shaped boxes can hold exactly the same volume — shape and volume are independent of each other.
Measure a shoebox's length, width and height, then calculate its volume in cubic centimetres.
Build a small cube from sugar cubes or blocks and count how many unit cubes fill it.
Loading questions…