Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Volume & Surface Area — exam questions
10 original Incandio exam-style questions on volume & Surface Area, 26 marks, about 31 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Volume & Surface Area — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
6 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Calculate (1–5 marks)
- a numerical answer obtained by calculation
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 4.10. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
A cube has edges of length 3 cm. Write down its volume.
volume = ............................ cm3
(Total for Question 1 = 1 mark)
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(2)Work out
A cylinder has a radius of 4 cm and a height of 10 cm. Work out its volume, to 1 decimal place.
volume = ............................ cm3
(Total for Question 2 = 2 marks)
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(2)Calculate
A cuboid measures 5 cm by 4 cm by 2 cm. Calculate its total surface area.
total surface area = ............................ cm2
(Total for Question 3 = 2 marks)
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(1)Explain why
The volume of any prism is the area of its cross-section multiplied by its length. Explain why this works for a cylinder as well as for a box.
(Total for Question 4 = 1 mark)
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(2)Calculate
A sphere has a radius of 6 cm. Calculate its volume, to the nearest cm³.
volume = ............................ cm3
(Total for Question 5 = 2 marks)
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(3)Find
A prism 15 cm long has a triangular cross-section with base 8 cm and perpendicular height 5 cm. Find its volume.
volume = ............................ cm3
(Total for Question 6 = 3 marks)
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(3)Show that
A closed cylinder has a radius of 3 cm and a height of 7 cm. Show that its total surface area is 60π cm².
(Total for Question 7 = 3 marks)
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(3)Work out
A cone has a base radius of 5 cm and a slant height of 13 cm. Work out its volume, to 3 significant figures.
volume = ............................ cm3
(Total for Question 8 = 3 marks)
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(4)Find
A cylindrical tin holds 1 litre and its base has a radius of 6 cm. Find its height, to 1 decimal place.
height = ............................ cm
(Total for Question 9 = 4 marks)
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(5)Work out
A solid cylinder has radius 4 cm and height 10 cm. It is melted down and recast as a cube. Work out the length of one edge of the cube.
edge length = ............................ cm
(Total for Question 10 = 5 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain volume & Surface Area to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Archimedes over three rounds, marked against descriptors you can read first.
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Back to the module
- Volume & Surface Area — Prisms, cylinders, spheres and cones — filling solids (volume) and wrapping them (surface area), including the formulas the sheet won't give you.
- All of Incandio Mathematics · Incandio Exam Practice