Mensuration is part of the Class 9 Mathematics syllabus for the AISSEE (Sainik School) entrance exam, where Maths carries 200 of 400 marks (50 questions × 4 marks), and for the RMS CET Class 9 paper. AISSEE 2027 is on Sunday, 31 January 2027, with no negative marking.
Area Formulas
Shape | Area | Perimeter |
|---|---|---|
Rectangle | l × b | 2(l + b) |
Square | a² | 4a |
Triangle | ½ × base × height | sum of sides |
Parallelogram | base × height | 2(a + b) |
Trapezium | ½ × (sum of parallel sides) × height | sum of sides |
Rhombus | ½ × d₁ × d₂ | 4 × side |
Circle | πr² | 2πr (circumference) |
Surface Area and Volume
Solid | Curved / lateral surface area | Total surface area | Volume |
|---|---|---|---|
Cuboid | 2h(l + b) | 2(lb + bh + hl) | l × b × h |
Cube | 4a² | 6a² | a³ |
Cylinder | 2πrh | 2πr(r + h) | πr²h |
Euler’s Formula
For any polyhedron: F + V − E = 2 (faces + vertices − edges). Cube: 6 + 8 − 12 = 2 ✔. Triangular prism: 5 + 6 − 9 = 2 ✔.
Units
1 m² = 10,000 cm²
1 cm³ = 1 mL; 1,000 cm³ = 1 litre
1 m³ = 1,000 litres
Solved Examples
Trapezium: parallel sides 10 cm and 6 cm, height 4 cm. Area = ½ × 16 × 4 = 32 cm².
Cylinder: r = 7 cm, h = 10 cm (π = 22/7). Volume = 22/7 × 49 × 10 = 1,540 cm³; curved surface area = 2 × 22/7 × 7 × 10 = 440 cm²; total surface area = 440 + 2 × 154 = 748 cm².
Cube: side 5 cm. Total surface area = 6 × 25 = 150 cm²; volume = 125 cm³.
Cuboid tank: 2 m × 1.5 m × 1 m holds 3 m³ = 3,000 litres.
Rhombus: diagonals 10 cm and 8 cm. Area = ½ × 10 × 8 = 40 cm².
Exam Tips
Use π = 22/7 when the radius is a multiple of 7.
Convert all measurements to the same unit before calculating.
Read carefully whether the question asks for curved or total surface area.
Practise and Revise
Mensuration MCQs (Class 9) — 10 questions with answers and explanations
Free AISSEE / RMS Mock Test
Enunciate Academy runs online coaching for Sainik School, RMS, Navodaya and RIMC entrance exams for Class 4 to 9 students across Andhra Pradesh and Telangana. Message us on WhatsApp (94924 44498) to get a free mock test, or see the Spark batch details.
