Maths Olympiad · topic 26 of 33 · free

Mensuration: circles, surface area and volume — Maths Olympiad practice

Mensuration questions test the right formula and the right units: centimetres for lengths, square centimetres for areas and cubic centimetres for volumes. With π = 22/7, choose radii in the 7 table and cancel the 7 first. When every length grows k times, areas grow k × k times and volumes k × k × k times.

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How to solve it

Divide by 7 first — “with π = 22/7 and a radius in the 7 table, cancel the 7 before multiplying”

Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first.
Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl).
Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

Use it for: Circle, cube, cuboid, tank and scaling questions in Class 7–10 Olympiad papers and mensuration chapters.

🧮 Check your own sums with the free Ratio calculator — it shows the working.

Worked example: What is the area of a circle of radius 14 cm? (Use π = 22/7.) → 616 sq cm

Area = π × r × r = 22/7 × 14 × 14.
14 ÷ 7 = 2, so 22 × 2 × 14 = 616.

Check: 616 × 7 = 4312 and 22 × 14 × 14 = 4312 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

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