L7 · Volume problem solving

Learning goal

“I can solve volume problems in context: comparing containers, finding how much space is left, and counting how many small cubes or boxes fit inside a bigger prism - checking that my units and my method make sense.”

Capacity — the volume a container can hold when completely full.

Remaining volume — the space left in a container: capacity minus what is already in it.

Fit — how many times a smaller volume divides exactly into a bigger one; the small solid's dimensions must divide the big prism's dimensions evenly for a clean fit.

Worked example

Box A is 6 cm x 4 cm x 3 cm. Box B is 5 cm x 5 cm x 3 cm. Which holds more, and by how much? Step 1: Never judge by one dimension - compute both volumes. Step 2: A: 6 x 4 x 3 = 72 cm3. B: 5 x 5 x 3 = 75 cm3. Step 3: B holds more, by 75 - 72 = 3 cm3. Say it plainly: comparing volumes means computing volumes, then comparing the numbers.

Check yourself — explain it

Box A is longer than Box B. Why is that not enough to say A holds more?

Paired problem — example still visible

Box C: 8 x 3 x 3. Box D: 9 x 4 x 2. -> C: 72 cm3; D: 72 cm3 - they hold exactly the same amount.

Faded completion — last step is yours

"A bin is 10 cm x 5 cm x 4 cm, so its capacity is ___ cm3. It already holds 150 cm3 of sand, so the space left is ___ cm3." -> 200 cm3; 50 cm3

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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