Mensuration
About 6 min · Mathematics and Science (Paper II) · English
Time worked out from the lesson's 383 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. For AP TET Paper II, this topic tests both conceptual understanding and computational accuracy across classes 6-8 content.
Key ideas
- Perimeter is the total length of the boundary of a 2D figure; Area is the measure of the region enclosed within that boundary.
- Surface Area of a 3D solid is the total area of all its outer faces—think of it as the amount of material needed to wrap the solid completely.
- Volume measures the space occupied by a 3D object—the capacity it can hold. Volume is always expressed in cubic units (cm³, m³).
- Lateral Surface Area (LSA) includes only the curved or side surfaces, excluding top and bottom faces. Total Surface Area (TSA) includes all faces.
- For composite figures, break the shape into standard components, calculate separately, then add or subtract as needed.
Watch out for
- Confusing radius and diameter → Always verify whether the problem gives radius (r) or diameter (d). If diameter is given, divide by 2 before applying formulas.
- Mixing up LSA and TSA → Read carefully whether the question asks for "curved surface area" (LSA) or "total surface area" (TSA). A closed cylinder needs TSA; an open tank needs LSA + one base.
- Using wrong height in cones → The formula uses perpendicular height (h) for volume but slant height (l) for curved surface area. Students often interchange these.
Quick reference
- Rectangle area = l × b; Perimeter = 2(l + b)
- Circle area = πr²; Circumference = 2πr
- Cylinder volume = πr²h; TSA = 2πr(r + h)
- Cone volume = ⅓πr²h; Slant height l = √(r² + h²)
- Sphere volume = (4/3)πr³; Surface area = 4πr²
Check yourself: 3 questions
1. A rectangular garden is 25 m long and 18 m wide. What is the area of the garden in square metres?
2. A cylindrical water tank has a radius of 7 m and a height of 10 m. What is the volume of the tank in cubic metres? (Use π = 22/7)
3. The perimeter of a square field is 160 m. What is the area of the field?
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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