Mathwright

Area, perimeter, volume & surface area

Area & Volume Workshop

Area and volume carry around 10% of the marks on IGCSE and GCSE papers, on every board and tier. Ten stations take students from area of 2D shapes to sectors, cones, spheres, similar solids and past-paper style problems (compound solids, melting and recasting, frustums), with Foundation/Core and Higher/Extended levels.

  • GCSE Foundation
  • GCSE Higher
  • IGCSE Core
  • IGCSE Extended
  • Ages 11–16

What students practise

  • Area and perimeter of rectangles, triangles, parallelograms and trapeziums
  • Circumference and area of circles, answers in terms of π
  • Compound shapes and shaded regions
  • Arc length and sector area
  • Volume of cuboids, prisms and cylinders
  • Surface area and nets
  • Cones, pyramids, spheres and hemispheres
  • Area, volume and capacity unit conversions, density
  • Similar shapes: lengths, plus area and volume scale factors at Higher
  • Exam problems: compound solids, melting and recasting, pouring water, packing boxes; frustums and density at Higher

How it works

Learn

20 short lessons, each labelled with the exams it is for, with a worked example and a quick check.

Practise

Ten stations, fresh questions each visit, with hints that fade.

Challenge

Mixed questions from every station with a station-by-station report.

For teachers

Open Teacher Options in the game to choose skills and levels. Nothing is uploaded: progress stays in each student's browser, so no accounts or data-protection paperwork are needed.

Which exams it covers

Every station is matched to the current specifications. Teacher options switch between Foundation/Core and Higher/Extended questions.

TopicGCSE (AQA, Edexcel)Cambridge IGCSE 0580
Area and perimeter of 2D shapesG16C5.2 / E5.2
Circles, arcs and sectorsG17, G18C5.3 / E5.3 (Core: sector angle a factor of 360°)
Compound shapes and parts of shapesG16, G17C5.5 / E5.5
Volume and surface area: prisms, cylinders, cones, pyramids, spheresG16, G17C5.4 / E5.4
Units of area, volume and capacity; densityG14, N13, R11C5.1 / E5.1
Similar shapes: lengthsG19C4.4 / E4.4
Similar shapes: areas and volumesG19 (Higher only)E4.4 (Extended only)
Compound solids, melting and recasting, pouring waterG16, G17C5.5 / E5.5
Frustums; density from displacementG17, R11 (Higher)E5.5; C/E1.12 (formula given)

Worked examples

Three examples of the kind of question the game generates, from Foundation/Core to Higher/Extended.

Sector Slice · Foundation / Core

A sector has radius 9 cm and angle 40°. Find its arc length and its area.

  1. 40/360 = 1/9 of the circle
  2. Arc length = 1/9 × 2 × π × 9 = 2π = 6.28 cm (3 s.f.)
  3. Area = 1/9 × π × 9² = 9π = 28.3 cm² (3 s.f.)

Answer: arc 6.28 cm, area 28.3 cm²

Pointed Solids · Foundation / Core

A cone has radius 6 cm and vertical height 8 cm. Find its volume and its curved surface area.

  1. Volume = ⅓ × π × 6² × 8 = 96π = 302 cm³ (3 s.f.)
  2. Slant height l = √(6² + 8²) = 10 cm
  3. Curved surface area = π × 6 × 10 = 60π = 188 cm² (3 s.f.)

Answer: 302 cm³ and 188 cm²

Scale Lab · Higher / Extended

Two similar solids have heights 5 cm and 15 cm. The smaller has volume 40 cm³ and surface area 64 cm². Find the volume and surface area of the larger.

  1. Length scale factor k = 15 ÷ 5 = 3
  2. Area factor k² = 9, so surface area = 64 × 9 = 576 cm²
  3. Volume factor k³ = 27, so volume = 40 × 27 = 1080 cm³

Answer: 1080 cm³ and 576 cm²

Common mistakes the game targets

  • Using the sloping side as the height. Triangles, parallelograms and cone volumes all need the perpendicular height.
  • Putting the diameter into πr². Halve it first. Using the diameter makes the area four times too big.
  • Forgetting the straight edges. The perimeter of a semicircle or sector includes the diameter or the two radii.
  • Converting area units by 100. 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³: square or cube the length factor.
  • Using k for areas and volumes. Areas of similar shapes scale by k², volumes by k³.
  • Rounding too early. Keep the full calculator value until the last step, then give 3 significant figures.

Questions teachers and parents ask

Is the game free?

Yes. It is free to use, with no account, no adverts and no tracking. Progress is saved only in the student's own browser.

Which exams does it cover?

GCSE Foundation and Higher (AQA and Edexcel) and Cambridge IGCSE 0580 Core and Extended. Teachers choose the level in Teacher options.

Does it have past-paper style questions?

Yes. The Exam Problems station has the multi-step types that appear on IGCSE and GCSE papers: compound solids, a sphere melted into a cylinder, water poured into a tank, boxes packed into a container, and at Higher, frustums and density from a falling water level. Every lesson shows which exam and tier it is for.

Which value of π does it use?

Either. Students can use the calculator value or 3.142, as Cambridge allows, and answers given in terms of π are marked as exact.

Does it work on phones and Chromebooks?

Yes. It runs in any modern browser on laptops, Chromebooks, tablets and phones, and works on a classroom board.

Are there printable worksheets to go with it?

Yes. Matching Mathwright worksheets and exam-style questions with full worked solutions are on the Resources page.

Matching worksheet packs

Printable practice and exam-style tests on the same topic, with full worked solutions.

Number

Measures & Accuracy: Error Intervals, Bounds, Rounding & Unit Conversions (AQA 8300)

Practice for Foundation and Higher tiers, with full worked solutions.

  • GCSE Foundation
  • GCSE Higher

Free practice: Area & Volume Workshop

Geometry, trigonometry & vectors

Mensuration — IGCSE 0580 Paper 2 & 4

Area, volume and surface area worksheets in the style of Paper 2 and Paper 4, with mark schemes.

  • IGCSE Extended

Free practice: Area & Volume Workshop

Need worksheets and lessons to go with the games?

Printable IGCSE and GCSE resources from Mathwright: worksheets, exam-style practice and full worked solutions.

Browse resources

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