Mensuration
About 6 min · Quantitative Ability · English
Time worked out from the lesson's 380 words at 150 words a minute, plus a minute for each question.
Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas, and volumes.
Key ideas
- Perimeter is the total length of the boundary of a 2D figure. Think of it as the length of fence needed to enclose a plot.
- Area measures the surface covered by a 2D figure. Think of it as the amount of paint needed to cover a floor.
- Surface Area of a 3D solid is the total area of all its outer faces. Curved Surface Area (CSA) excludes the flat ends (bases), while Total Surface Area (TSA) includes everything.
- Volume measures the space occupied by a 3D solid. Think of it as the amount of water a container can hold.
- Unit consistency is critical: if dimensions are in metres, area is in m² and volume is in m³. Convert all dimensions to the same unit before calculating.
Watch out for
- Confusing CSA with TSA: Students use total surface area when only curved surface is asked (e.g., painting the lateral surface of a cylinder). → Always check whether the question asks for CSA or TSA.
- Forgetting unit conversion: Mixing cm and m in the same problem leads to answers off by powers of 10 or 100. → Convert all measurements to the same unit first.
- Using diameter instead of radius: Many questions give diameter, but all formulas use radius. → Divide diameter by 2 immediately when you read the problem.
Quick reference
- Rectangle area = l × b; Perimeter = 2(l + b)
- Circle area = πr²; Circumference = 2πr
- Volume of cube = a³; TSA = 6a²
- Volume of cylinder = πr²h; CSA = 2πrh
- Volume of sphere = (4/3)πr³; Surface area = 4πr²
Check yourself: 3 questions
1. A rectangular field is 75 metres long and 40 metres wide. What is the cost of fencing it at the rate of Rs 12 per metre?
2. The area of a square field is 2304 square metres. Find the cost of fencing it at Rs 15 per metre.
3. A cylindrical water tank has a radius of 7 metres and a height of 10 metres. What is the volume of water it can hold? (Use π = 22/7)
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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