Last reviewed: 25 October 2026
Volume and capacity questions are practical, which is why they appear so often in revision papers: water tanks, boxes, jerricans and classrooms all need them. This guide covers the formulas, the conversions that trip learners up, and the real-life problems that tie it all together. It suits upper primary learners revising cubes and cuboids and junior school learners adding cylinders. Volume of solids is a Measurements sub-strand in KICD’s Grade 9 Mathematics curriculum design.
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Volume Versus Capacity
Volume is the amount of space an object takes up, measured in cubic units such as cm³ or m³. Capacity is how much a container can hold, usually measured in millilitres and litres. They are linked by one key fact: 1,000 cm³ = 1 litre, and so 1 cm³ = 1 ml.
Cubes and Cuboids
A cuboid’s volume is length × width × height. A box 20 cm long, 10 cm wide and 8 cm high has a volume of 1,600 cm³. A cube has all edges equal, so its volume is side × side × side. A cube of side 5 cm has a volume of 125 cm³.
Questions often work backwards. A cuboid has a volume of 480 cm³, length 12 cm and width 8 cm. Its height is 480 ÷ (12 × 8) = 480 ÷ 96 = 5 cm.
Cylinders
A cylinder has a circular cross-section. Its volume is the area of the circle times the height: V = πr²h, where r is the radius. Use π = 22/7 or 3.142 as the question instructs.
- A cylinder with radius 7 cm and height 10 cm: V = 22/7 × 7 × 7 × 10 = 1,540 cm³, which is 1.54 litres.
- A tin with diameter 14 cm and height 20 cm: the radius is 7 cm, so V = 22/7 × 49 × 20 = 3,080 cm³.
The commonest mistake is using the diameter instead of the radius. Always halve the diameter first.
Conversions You Must Know
- 1 litre = 1,000 ml = 1,000 cm³
- 1 m³ = 1,000,000 cm³ = 1,000 litres
- 1 cm = 10 mm, so 1 cm³ = 1,000 mm³
The jump from m³ to cm³ surprises learners. A cube 1 m on each side is 100 cm × 100 cm × 100 cm, which is 1,000,000 cm³, not 100 cm³.
Water Tank Problems
- A rectangular tank is 2 m long, 1.5 m wide and 1 m high. Volume = 3 m³, so it holds 3,000 litres.
- A cylindrical tank has radius 0.7 m and height 2 m. V = 22/7 × 0.49 × 2 = 3.08 m³, which is 3,080 litres.
- If a family uses 140 litres a day, a full 3,080-litre tank lasts 3,080 ÷ 140 = 22 days.
Filling and Pouring Problems
“How many 500 ml bottles can be filled from a 20 litre container?” Convert to the same unit: 20,000 ml ÷ 500 ml = 40 bottles. “A tap fills a 1,500 litre tank at 25 litres per minute. How long does it take?” 1,500 ÷ 25 = 60 minutes.
Surface Area: Do Not Confuse It
Surface area is the total area of all the faces, in square units, and answers questions such as how much paper wraps a box. Volume is how much fits inside, in cubic units. Reading the question carefully for words like “wrap”, “paint” or “cover” (surface area) versus “hold”, “fill” or “contain” (volume) prevents this mix-up.
Practice Routine
Measure real containers at home, calculate their volumes, and check by filling them with water using a measuring jug. Then move to exam questions. The exam countdown gives five free questions a day and the What to Revise report shows remaining gaps. Related guides: area and perimeter and Pythagoras’ theorem. Full papers with worked answers are in the Monthly Pass (KSh 500 by M-Pesa).