Class 8 Mathematics Chapter 9 Mensuration

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I. Chapter Summary:

The chapter Mensuration focuses on the measurement of 2D and 3D geometrical shapes. It introduces students to calculating areas, surface areas, and volumes of different solid shapes like cubes, cuboids, cylinders, cones, and spheres. Students also learn to convert units, apply formulas practically, and solve real-life problems based on dimensions and capacities.

II. Key Concepts Covered:

Concept	Explanation
Area of Trapezium & General Quadrilateral	Area calculated using average of parallel sides × height.
Area of Polygons	Breakdown into triangles or trapeziums for calculation.
Surface Area	Total area covering the surface of 3D objects (cuboid, cylinder).
Volume	Amount of space occupied by a 3D object.
Volume of Cube & Cuboid	Using side × side × side or length × breadth × height.
Volume of Cylinder	$$πr2h\pi r^2 h$ ; space occupied inside a cylinder.
Conversion of Units	Changing cm³ to m³, litre to m³, etc.
Applications	Real-world problems involving tanks, rooms, boxes, and containers.

III. Important Questions

(A) Multiple Choice Questions (1 Mark)

The volume of a cuboid with dimensions 5 cm × 4 cm × 3 cm is:
a) 60 cm³
b) 45 cm³
c) 30 cm³
d) 50 cm³
Ans: a) 60 cm³
Surface area of a cube of side 6 cm is:
a) 36 cm²
b) 216 cm²
c) 96 cm²
d) 144 cm²
Ans: b) 216 cm²
(PYQ 2020) The volume of a cube of side 7 cm is:
a) 343 cm³
b) 49 cm³
c) 210 cm³
d) 294 cm³
Ans: a) 343 cm³
The area of trapezium with parallel sides 8 cm and 12 cm and height 5 cm is:
a) 40 cm²
b) 50 cm²
c) 60 cm²
d) 100 cm²
Ans: c) 50 cm²

(B) Short Answer Questions (2–3 Marks)

Find the volume of a cylinder with radius 4 cm and height 10 cm. Use $π=3.14\pi = 3.14$ .
A cube has surface area of 150 cm². Find the side of the cube.
(PYQ 2019) Find the total surface area of a cuboid of dimensions 5 cm × 3 cm × 2 cm.
Convert 1.5 m³ into litres.

(C) Long Answer Questions (5 Marks)

A water tank is in the shape of a cuboid with dimensions 6 m × 5 m × 4 m. How many litres of water can it hold?
The inner diameter of a cylindrical container is 14 cm and height is 10 cm. Find the cost of painting the inner surface at ₹2 per cm².
(PYQ 2018) A cuboidal wooden box has dimensions 1.2 m × 0.8 m × 0.5 m. Find the volume in litres.
A cone is melted to form a cylinder. If the height and radius of the cone are 12 cm and 6 cm respectively, find the radius of the cylinder formed assuming the height is 9 cm.

(D) HOTS (Higher Order Thinking Skills)

A cube is painted on all six faces and then cut into 64 small equal cubes. How many cubes will have exactly 2 painted faces?
A container is shaped like a cuboid of size 60 cm × 40 cm × 30 cm. If water is poured into it at the rate of 500 mL/sec, how long will it take to fill it completely?

IV. Key Formulas / Concepts

Quantity	Formula
Area of Trapezium	$12(a+b)h\frac{1}{2}(a + b)h$
Volume of Cube	$a^3$
Volume of Cuboid	$l \times b \times h$
Volume of Cylinder	$πr2h\pi r^2 h$
Surface Area of Cube	$6a^2$
Surface Area of Cuboid	$2 (l b + bh + h l)$
Curved Surface Area of Cylinder	$2πrh2\pi rh$
Total Surface Area of Cylinder	$2πr(h+r)2\pi r(h + r)$
1 m³	1000 litres
$π\pi$	Take 3.14 or $227\frac{22}{7}$

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

Unit/Chapter	Estimated Marks	Type of Questions Typically Asked
Mensuration	8–10 Marks	Word problems, applications, diagrams, HOTS

VII. Previous Year Questions (PYQs)

Year	Marks	Question
2020	1 mark	Volume of cube with side 7 cm
2019	3 marks	Surface area of cuboid (5 cm × 3 cm × 2 cm)
2018	5 marks	Volume of wooden box and conversion into litres
2017	2 marks	Area of trapezium with given dimensions

VIII. Real-World Application Examples

Architecture: Estimating the amount of material (cement, bricks) required to build structures.
Water Conservation: Calculating water usage in tanks, reservoirs, and pipes.
Packaging Industry: Determining volume for packing boxes, bottles, and cans.
Transport: Volume helps calculate capacity of containers used in trucks and ships.

IX. Student Tips & Strategies for Success (Class 8 Specific)

Time Management:

Practice mensuration daily for 20–30 minutes.
Use diagrams for better clarity in surface area and volume.

Exam Preparation:

Focus on formula memorization with a formula chart.
Solve practical word problems from real scenarios.

Stress Management:

Use real objects (boxes, bottles) to visualize concepts.
Stay calm and revise topics weekly instead of cramming.

X. Career Guidance & Exploration

For Classes 9–10:

Streams Preview: Math-intensive careers like Engineering, Architecture, and Data Science need geometry and measurement understanding.
Olympiads/NTSE: Mensuration problems are common in logical reasoning and quant sections.

For Classes 11–12:

Competitive Exams: JEE, CUET, NDA, NEET (basic volume formulas).
Career Paths:
- Civil Engineer
- Architect
- Surveyor
- Interior Designer
- Naval Engineer

XI. Important Notes

Practice with unit conversion—litres to cm³/m³ etc.
Learn to draw clean diagrams with labelled dimensions.
Highlight units in all your answers (cm², m³, etc.)—they matter in exams.

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