Last reviewed: 11 November 2026
Updated November 2026. These Grade 7 volume and capacity notes show how to use the cubic metre as a unit of volume, how to convert between m3 and cm3, how to find the volume of cubes, cuboids and cylinders, and how volume relates to the capacity of a container in litres. Volume is the space a solid occupies. Capacity is how much liquid a container can hold. 1 000 cm3 of water fills a 1 litre bottle.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 7 Mathematics measurements sub-strand on volume and capacity in the KICD Grade Seven curriculum designs. Pyramids, cones, frustums and spheres come later, in the Grade 9 volume of solids notes. For Grade 7 topics overall, use the Grade 7 mathematics revision guide and the Grade 7 notes hub.
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Cubic Metres, Cubic Centimetres and Litres
The SI unit of volume is the cubic metre. A cube with edges of 1 m has volume 1 m3. Each edge of that cube is 100 cm, so 1 m3 = 100 × 100 × 100 = 1 000 000 cm3. The litre is accepted for use with SI: 1 litre = 1 dm3 = 1 000 cm3, as noted on the NIST page on SI units of volume. Therefore 1 m3 = 1 000 litres.
Worked example: conversions
2.5 m3 = 2.5 × 1 000 000 = 2 500 000 cm3 = 2 500 litres.
A jerrycan labelled 20 litres has a capacity of 20 × 1 000 = 20 000 cm3, which is 0.02 m3.
Volume of Cubes, Cuboids and Cylinders
Volume of a cube = s3. Volume of a cuboid = l × w × h. Volume of a cylinder = πr2h, the area of the circular end multiplied by the height. The same three formulas appear in OpenStax Prealgebra’s section on volume and surface area. Capacity of a container is the volume of liquid it can hold, so once you have the volume in cm3 you can write it in litres by dividing by 1 000.
Worked example
A wooden cube has side 8 cm. Volume = 8 × 8 × 8 = 512 cm3.
A rectangular water tank measures 10 cm by 6 cm by 4 cm internally. Volume = 10 × 6 × 4 = 240 cm3 = 0.24 litres.
A cylindrical tin has radius 7 cm and height 10 cm. Taking π = 22/7, volume = (22/7) × 49 × 10 = 22 × 7 × 10 = 1 540 cm3 = 1.54 litres.
Original Practice Questions With Worked Answers
- Convert 3 m3 to cm3 and to litres. 3 000 000 cm3 = 3 000 litres.
- A cube has side 5 cm. Find its volume. 125 cm3.
- A cuboid measures 12 cm by 5 cm by 8 cm. Find its volume in litres. 480 cm3 = 0.48 litres.
- A cylinder has radius 14 cm and height 5 cm. Taking π = 22/7, find its volume. (22/7) × 196 × 5 = 22 × 28 × 5 = 3 080 cm3.
- A 5 litre container is filled from a tap that delivers 250 cm3 each second. How many seconds are needed? 5 litres = 5 000 cm3; 5 000 ÷ 250 = 20 seconds.
- A learner writes 1 m3 = 10 000 cm3. What was forgotten? Volume scales with the cube of the length. 100 × 100 × 100 = 1 000 000, not 100 × 100.
Cover the answers and try each question. Length conversions that feed these calculations are in the Grade 7 length notes, and the metric unit converter can check them. A broader junior-school recap is at volume and capacity revision. For timed practice use the Grade 7 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the difference between volume and capacity?
Volume is the space a solid occupies, measured in cubic units such as cm3 or m3. Capacity is how much a container can hold, often written in litres. They describe the same amount of space in different units: 1 000 cm3 = 1 litre.
How many cm3 are in 1 m3?
1 000 000 cm3, because each of the three edges of a 1 m cube is 100 cm long and 100 × 100 × 100 = 1 000 000.
How do you find the volume of a cylinder?
Use V = πr2h. A tin of radius 7 cm and height 10 cm has volume 1 540 cm3 when π = 22/7, which is 1.54 litres.
How do you change cm3 to litres?
Divide by 1 000, because 1 litre = 1 000 cm3. 240 cm3 = 0.24 litres.