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Cambridge IGCSE Maths (0580) · Topic 5: Mensuration · 5.4

Cambridge IGCSE Maths 0580 Surface Area and Volume Questions

Surface Area and Volume questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise surface area and volume →Surface Area and Volume notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Surface Area and Volume questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

A cuboid measures \(5\) cm by \(4\) cm by \(3\) cm.
Work out (a) its volume (b) its surface area.

Show the worked answer
  1. (a) \(5 \times 4 \times 3 = 60\) cm³
  2. (b) \(2(5 \times 4 + 5 \times 3 + 4 \times 3) = 2(20 + 15 + 12) = 94\) cm²

Answer: (a) \(60\) cm³ (b) \(94\) cm²

Question 2 Core calculator · easy

A cylinder has radius \(3\) cm and height \(10\) cm.
Work out its volume, correct to 3 significant figures.

Show the worked answer
  1. \(V = \pi r^2 h = \pi \times 9 \times 10 = 90\pi = 282.7\ldots\) cm³

Answer: \(283\) cm³

Question 3 Core calculator · easy · 2 marks

A cylinder has radius 4 cm and height 10 cm. Find its volume. Give your answer correct to 3 significant figures.

Show the answer and mark scheme
  • M1 π × 4² × 10
  • A1 503 cm³ (502.6…)

Answer: \(503\text{ cm}^3\)

Question 4 Core calculator · medium

A prism is \(15\) cm long. Its cross-section is a triangle with base \(6\) cm and perpendicular height \(4\) cm.
Work out its volume.

Show the worked answer
  1. Area of cross-section \(= \frac{1}{2} \times 6 \times 4 = 12\) cm².
  2. Volume \(= 12 \times 15 = 180\) cm³.

Answer: \(180\) cm³

Question 5 Core calculator · medium

A sphere has radius \(6\) cm.
Work out its volume, correct to 3 significant figures. (\(V = \frac{4}{3}\pi r^3\))

Show the worked answer
  1. \(\frac{4}{3} \times \pi \times 216 = 288\pi = 904.7\ldots\) cm³

Answer: \(905\) cm³

Question 6 Core calculator · medium

A cone has base radius \(5\) cm, perpendicular height \(12\) cm and slant height \(13\) cm.
Work out (a) its volume (b) its curved surface area. Give each answer correct to 3 significant figures. (\(V = \frac{1}{3}\pi r^2 h\), curved surface area \(= \pi r l\))

Show the worked answer
  1. (a) \(\frac{1}{3} \times \pi \times 25 \times 12 = 100\pi = 314.1\ldots\) cm³
  2. (b) \(\pi \times 5 \times 13 = 65\pi = 204.2\ldots\) cm²

Answer: (a) \(314\) cm³ (b) \(204\) cm²

Question 7 Core non-calculator · medium · 2 marks

A cone has radius 3 cm and height 8 cm. The volume of a cone is \(\frac{1}{3}\pi r^2 h\). Find its volume in terms of \(\pi\).

Show the answer and mark scheme
  • M1 ⅓ × π × 3² × 8
  • A1 24π cm³

Answer: \(24\pi\text{ cm}^3\)

Question 8 Core calculator · medium · 3 marks

A sphere has radius 6 cm. The volume of a sphere is \(\frac{4}{3}\pi r^3\) and its surface area is \(4\pi r^2\). Find

(a) its volume (b) its surface area.

Give your answers correct to 3 significant figures.

Show the answer and mark scheme
  • M1 4/3 × π × 6³ or 4 × π × 6²
  • A1 (a) 905 cm³ (904.7…)
  • A1 (b) 452 cm² (452.3…)

Answer: (a) \(905\text{ cm}^3\) (b) \(452\text{ cm}^2\)

Question 9 Core calculator · hard

A pyramid has a square base of side \(9\) cm and a perpendicular height of \(10\) cm.
Work out its volume. (\(V = \frac{1}{3} \times\) base area \(\times\) height)

Show the worked answer
  1. Base area \(= 81\) cm².
  2. \(\frac{1}{3} \times 81 \times 10 = 270\) cm³

Answer: \(270\) cm³

Question 10 Core calculator · hard

A cylinder has a volume of \(500\) cm³ and a radius of \(5\) cm.
Find its height, correct to 3 significant figures.

Show the worked answer
  1. \(\pi \times 25 \times h = 500\)
  2. \(h = \frac{500}{25\pi} = 6.366\ldots\) cm

Answer: \(6.37\) cm

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test surface area and volume?

Surface Area and Volume is on both tiers (syllabus 5.4), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more surface area and volume questions?

In the 0580 practice for topic 5 (Mensuration), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More mensuration questions