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Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

IGCSE Maths Volume and Surface Area Questions and Answers

Volume and Surface Area questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

Practise volume and surface area in Unit 5 →Volume and Surface Area revision notes

What this topic covers

Volume and Surface Area worked examples

Worked example 1: Volume of a prism

A triangular prism has a cross-section with base 6 cm and height 4 cm, and length 15 cm. Find its volume.

Solution

  1. Cross-section area: \(\tfrac{1}{2}\times6\times4=12\).
  2. Volume \(=12\times15=180\) cm³.

Answer: 180 cm³

Tip: Volume of a prism = area of cross-section × length.

Worked example 2: Surface area of a cylinder

Find the total surface area of a closed cylinder with radius 5 cm and height 8 cm.

Solution

  1. Two circles: \(2\pi\times25=50\pi\).
  2. Curved surface: \(2\pi\times5\times8=80\pi\).
  3. Total \(130\pi=408\) cm² (3 s.f.).

Answer: \(130\pi\approx408\) cm²

Tip: The curved surface unrolls to a rectangle 2πr by h.

Worked example 3: Volume of a sphere

Find the volume of a sphere of radius 4.5 cm.

Solution

  1. \(V=\tfrac{4}{3}\pi r^3=\tfrac{4}{3}\pi\times91.125\).
  2. \(=382\) cm³ (3 s.f.).

Answer: 382 cm³

Tip: Cube the radius before multiplying.

Volume and Surface Area exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

A cube has edges of length 4 cm. Work out its total surface area.

Show the answer and mark scheme
  • M1 6 × 4²
  • A1 96 cm²

Answer: 96 cm²

Question 2 · medium · 3 marks

A triangular prism has a cross-section that is a right-angled triangle with sides 6 cm, 8 cm and 10 cm. The prism is 15 cm long. Work out its total surface area.

Show the answer and mark scheme
  • M1 2 × ½ × 6 × 8 (= 48)
  • M1 15 × (6 + 8 + 10) (= 360)
  • A1 408 cm²

Answer: 408 cm²

Question 3 · hard · 3 marks

A cuboid has a square base of side 6 cm and a volume of 360 cm³. Work out its total surface area.

Show the answer and mark scheme
  • M1 height 360 ÷ 36 = 10
  • M1 2 × 36 + 4 × 6 × their 10
  • A1 312 cm²

Answer: 312 cm²

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise volume and surface area for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test volume and surface area?

Either Higher tier paper, 1H or 2H, can test volume and surface area: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more volume and surface area questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 5 topics: Geometry