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Volume and Capacity: 1 mL = 1 cm³

Maths · Stage 3
Year 5
Lesson Guide
Explanation
The volume of a box is the number of centimetre cubes that fill it: length times width times height. A four by three by two box has a bottom layer of twelve cubes and two layers, twenty-four cubic centimetres. Multiply in whichever order gives round numbers. And backwards: a volume of two hundred with a base of eight by five means a height of two hundred divided by forty, five.
Your Turn
Volume of a 5 by 2 by 3 box, and of a 3 by 3 by 3 cube. Check: 30 cm3; 27 cm3.
Watch Out
Three lengths, multiplied. Adding them, or multiplying only two, is the mistake. Units are cm3, cubed, because three lengths went in.
Explanation
A cube one centimetre on each side holds exactly one millilitre. That single fact links volume to capacity: a container's volume in cubic centimetres is its capacity in millilitres. A box eight by five by four has volume one hundred and sixty cubic centimetres and holds one hundred and sixty millilitres. A ten by ten by six box holds six hundred millilitres, which is zero point six litres.
Your Turn
A box is 10 × 10 × 6 cm. Its volume, and its capacity in litres? Check: 600 cm3; 0.6 L.
Watch Out
cm3 and mL are the same size. cm3 and L are not: 600 cm3 is 0.6 L, not 600 L.
Explanation
A litre is a thousand millilitres, so it is a thousand cubic centimetres — a ten by ten by ten cube, about the size of a milk carton. To turn cubic centimetres into litres, divide by a thousand: a tank thirty by twenty by ten is six thousand cubic centimetres, six litres. Many different boxes hold a litre, any whose sides multiply to a thousand — twenty by ten by five as well as the cube.
Your Turn
A tank is 30 × 20 × 10 cm. Volume in cm3, and litres? Check: 6 000 cm3; 6 L.
Watch Out
A 10 cm cube holds a litre. A cube of side 100 cm holds a thousand litres — a thousand times more, not ten.
Explanation
When the cubes are bigger than a centimetre, count how many fit along each edge, rounding down, and multiply the three counts. Two-centimetre cubes in a twenty by ten by five box: ten along, five across, and only two up, because five centimetres holds two of them with a centimetre to spare. One hundred cubes. Dividing the volumes — a thousand divided by eight — gives one hundred and twenty-five and is wrong, because the wasted centimetre layer holds nothing. Count the edges.
Your Turn
How many 3 cm cubes fit in a 12 × 9 × 7 box? Check: 4 × 3 × 2 = 24.
Watch Out
Round DOWN along each edge. 7 cm holds two 3 cm cubes, not 2.33 of them.
Explanation
Three questions look alike and end differently. How many millilitres a box holds is its volume in cubic centimetres. How many litres is that divided by a thousand. How many cubes of a given size fit is a count along each edge. And a missing side is the volume divided by the product of the other two. Read the last line of the question to see which is being asked. Quiz and exercises now.
Your Turn
A box 8 × 5 × h has volume 200 cm3. What is h? Check: 200 ÷ 40 = 5 cm.
Watch Out
"How many cubes" and "what volume" are different questions with different units. Cubes are a count; volume is cm3.
📌 Key Points — this lesson in a nutshell
  • Volume of a box = length × width × height, in cubic centimetres: cm3.
  • 1 cm3 holds 1 mL. So a box's volume in cm3 is its capacity in mL.
  • 1 L = 1 000 mL = 1 000 cm3 — a 10 × 10 × 10 cm cube.
  • Bigger cubes in a box: count how many fit along each edge, then multiply. 2 cm cubes in a 20 × 10 × 5 box: 10 × 5 × 2 = 100 — not 1 000 ÷ 8 in your head.
Step 1: Introduction
Step 1 of 5
A 4 by 3 by 2 box 4cm2cm3cm one layer: 4 × 3 = 12 cubes 2 layers: 12 × 2 = 24 cubes volume = 4 × 3 × 2 = 24 cm3 Layers of centimetre cubes: the bottom layer is length × width, and there are "height" layers. 5 × 2 × 3 = 30 cm3. 8 × 5 × 4 = 160 cm3. 3 × 3 × 3 = 27 cm3. Multiply in any order: 8 × 5 first is 40, then × 4. Pick the pair that makes a round number. Reverse: volume 200 with a base of 8 × 5 = 40 → height 200 ÷ 40 = 5.
1 cm3 = 1 mL 1cm1cm1cm a cube 1 cm on each side holds exactly 1 millilitre So a container's volume in cm3 IS its capacity in mL. A 250 cm3 container holds 250 mL. A box 8 × 5 × 4 has volume 160 cm3 and holds 160 mL. A 10 × 10 × 6 box: 600 cm3 = 600 mL = 0.6 L. Volume is the space; capacity is what it holds. For a box they are the same number in cm3 and mL. The Year 4 lesson said this; from here on it is used.
1 L = 1 000 mL = 1 000 cm3 10cm10cm10cm 10 × 10 × 10 = 1 000 cm3 = 1 000 mL = 1 litre a milk carton is about this size To convert cm3 to litres, ÷ 1000. A tank 30 × 20 × 10 = 6 000 cm3 = 6 L. 2 L = 2 000 cm3. 2.5 L = 2 500 cm3. A 20 × 10 × 5 box = 1 000 cm3 = exactly 1 L, a different shape from the cube. Many boxes hold a litre: any whose three sides multiply to 1 000. 20 × 10 × 5, 25 × 8 × 5, 50 × 10 × 2 … Size check: a litre is a cube you could hold in both hands.
How many 2 cm cubes fit in a 20 × 10 × 5 box? 20cm5cm10cm along 20 cm: 20 ÷ 2 = 10 cubes along 10 cm: 5 cubes up 5 cm: 2 cubes (with 1 cm to spare) 10 × 5 × 2 = 100 cubes Count how many fit along EACH edge — rounding down — then multiply the three counts. Dividing the volumes, 1 000 ÷ 8 = 125, is wrong here: the 5 cm height only fits 2 cubes, wasting a 1 cm layer. When every edge divides exactly, the two methods agree. When one does not, count the edges. 3 cm cubes in a 12 × 9 × 7 box: 4 × 3 × 2 = 24 (the 7 fits only two 3s).
Reading the question A box 10 × 10 × 10 cm. How many mL does it hold?1 000 mL A tank 30 × 20 × 10 cm. Litres?6 L A box 8 × 5 × ? has volume 200 cm3. Height?5 cm How many 2 cm cubes in a 20 × 10 × 5 box?100 "How many mL" → volume in cm3. "Litres" → ÷ 1000. "How many cubes" → count the edges. Three questions that look alike and need three different last steps. Quiz and exercises now.
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