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.

How to solve it

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

  1. Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first.
  2. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl).
  3. 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.

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

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

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

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

Right: 0 · Tried: 0

🏁 Topic 26 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the ⭕ Circle Champion badge when you pass — and a certificate when you finish all 13 topics of Part 4 · Class 5–10 problem solving. You can still take the test without signing in.

🖨️ Mensuration Worksheet for Maths Olympiad

✨ Free AI tutor

Ask the AI tutor about this topic

Why does it work? When should you use it? Ask in English, मराठी or हिंदी.

Sign in with Google to ask Free — 20 questions a day.

👩‍🏫 Maths Olympiad classes near you — online or at home

Prefer a real teacher? TalentJR teachers take live online classes anywhere in India and visit homes in selected cities. Tell us what you need and our team will call you with timings and fees.

Live online classesSmall groups or 1:1 with a teacher, from home, any city.
Teacher at homeA TalentJR teacher visits your home (selected cities).
At a centreClasses at a TalentJR partner centre near you, where available.
Badges, certificates & gifts A badge for every topic you pass, a certificate for every part you finish, plus TalentJR Points for daily practice. Mental maths Faster calculation helps in Olympiads — try Mental Maths Mastery.