IGCSE Mathematics: Volume and Surface Area Practice Questions
The volume of any prism is the cross sectional area multiplied by the length. Cones and pyramids take one third of the equivalent prism, and a sphere has volume four thirds pi r cubed.
Topic 5.4 of Cambridge IGCSE Mathematics 0580 supplies formulas that are printed on the front of the paper, so the marks come from choosing the right one and reading whether the surface area required is curved or total. The questions below test that distinction.
What you need to know for Volume and Surface Area
- PrismVolume = cross sectional area x length. A cylinder is a prism with a circular cross section, so its volume is pi r2 h.
- Cylinder surface areaCurved surface area = 2 pi r h. Total surface area adds the two circular ends: 2 pi r h + 2 pi r2.
- ConeVolume = one third pi r2 h, using the perpendicular height. Curved surface area = pi r l, using the slant height l.
- SphereVolume = four thirds pi r3. Surface area = 4 pi r2.
- Perpendicular versus slant heightVolume of a cone uses the perpendicular height. Curved surface area uses the slant height. They are linked by Pythagoras.
- UnitsVolume uses cm3 or m3. Surface area uses cm2 or m2. Capacity in litres relates to volume, with 1000 cm3 equal to 1 litre.
IGCSE Mathematics Volume and Surface Area questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
A cylinder has a radius of 5 cm and a height of 12 cm. Calculate its volume, correct to 3 significant figures.
Show the worked answer
- A cylinder is a prism, so volume = cross sectional area x height = pi r2 h.
- The cross sectional area is pi x 52 = pi x 25 = 78.54 cm2.
- Volume = 78.54 x 12 = 942.48 cm3.
- To 3 significant figures the volume is 943 cm3.
For the same cylinder, radius 5 cm and height 12 cm, calculate the curved surface area and the total surface area, correct to 3 significant figures.
Show the worked answer
- Curved surface area = 2 pi r h = 2 x pi x 5 x 12 = 376.99 cm2, which is 377 cm2.
- The two circular ends each have area pi r2 = pi x 25 = 78.54 cm2.
- Two ends contribute 2 x 78.54 = 157.08 cm2.
- Total surface area = 376.99 + 157.08 = 534.07, which is 534 cm2 to 3 significant figures.
A cone has a radius of 6 cm and a perpendicular height of 8 cm. Calculate its volume and its curved surface area, correct to 3 significant figures.
Show the worked answer
- Volume = one third pi r2 h = one third x pi x 36 x 8.
- one third x 288 = 96, so volume = 96 pi = 301.59, which is 302 cm3.
- Curved surface area needs the slant height, found by Pythagoras from the radius and the perpendicular height.
- l = the square root of (62 + 82) = the square root of 100 = 10 cm.
- Curved surface area = pi r l = pi x 6 x 10 = 188.50, which is 188 cm2 to 3 significant figures.
A sphere has a radius of 3 cm. Calculate its volume and its surface area, correct to 3 significant figures.
Show the worked answer
- Volume = four thirds pi r3 = four thirds x pi x 27.
- four thirds x 27 = 36, so volume = 36 pi = 113.10, which is 113 cm3.
- Surface area = 4 pi r2 = 4 x pi x 9 = 36 pi = 113.10 cm2.
- Both come to 113, which happens only because r = 3. The units differ, cm cubed and cm squared, so the answers are not the same quantity.
Common mistakes in this topic
- Using the slant height in a cone volume calculation, or the perpendicular height in the curved surface area.
- Forgetting the circular ends when a total surface area is required.
- Confusing pi r squared with 2 pi r.
- Giving a volume answer in cm squared.
- Cubing incorrectly in the sphere volume formula.
Exam tips
- The formulas are printed on the front of the paper. Practise finding the right one quickly rather than memorising them.
- Read carefully whether curved or total surface area is required, and whether the solid is open or closed.
- For any cone question, work out whether you need the perpendicular height or the slant height before you begin.
- Keep answers in terms of pi through the working and convert to a decimal only at the end.
- Check the unit: cubed for volume, squared for surface area.
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Volume and Surface Area FAQs
What is the volume of a cylinder?
Pi multiplied by the radius squared, multiplied by the height. A cylinder is a prism with a circular cross section, so the volume is simply the area of the circular end multiplied by the length or height of the cylinder.
What is the difference between curved and total surface area?
Curved surface area covers only the curved part of the solid. Total surface area adds the flat faces, meaning the two circular ends of a closed cylinder or the circular base of a cone. Read whether the solid is open or closed before deciding.
Which height do I use for a cone?
Use the perpendicular height for the volume and the slant height for the curved surface area. If only one is given, find the other using Pythagoras, since the radius, perpendicular height and slant height form a right-angled triangle.
How do volume and capacity relate?
Capacity is the volume a container can hold. One thousand cubic centimetres equals one litre, and one cubic metre equals one thousand litres. Convert your volume answer to the unit the question asks for before writing the final line.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.