Class 9 Mathematics Chapter 9 Mensuration MCQ Quiz – 30 Questions with Solutions

The revised CBSE assessment framework has shifted towards objective-type questions because they test quick recall, formula application, and logical reasoning—skills essential for modern competitive exams. Unlike long-answer questions, MCQs demand precision: a single miscalculation or formula slip costs full marks. Mensuration, with its diverse formulas and real-world applications, is a prime target for MCQ-heavy question papers. For example, a typical Class 9 Mensuration exam now includes 25–35% MCQs, each worth 1–2 marks. Mastering MCQs in Mensuration means: • Speed: Solve 30 questions in under 45 minutes with practice. • Accuracy: Avoid careless errors by eliminating trap options systematically. • Conceptual clarity: MCQs expose gaps instantly—if you guess, you haven't understood the formula. • Confidence: Repeated exposure to varied scenarios builds problem-solving muscle memory. Research shows students who practise MCQs for 2–3 weeks improve their paper accuracy by 15–20%. The key is not random guessing but deliberate practice with detailed feedback on every wrong answer.

These questions test basic formula recall and straightforward single-step calculations. They form the foundation for harder problems. **Q1.** The area of a trapezium with parallel sides 8 cm and 6 cm, and height 5 cm, is: (A) 35 cm² (B) 40 cm² (C) 70 cm² (D) 42 cm² **Answer:** (A) 35 cm² | **Reason:** Area = ½(a + b) × h = ½(8 + 6) × 5 = 35 cm² **Q2.** The surface area of a cube with side length 4 cm is: (A) 64 cm² (B) 96 cm² (C) 128 cm² (D) 48 cm² **Answer:** (B) 96 cm² | **Reason:** Surface area = 6a² = 6 × 4² = 96 cm² **Q3.** A cuboid has length 10 cm, breadth 8 cm, and height 6 cm. Its volume is: (A) 240 cm³ (B) 360 cm³ (C) 480 cm³ (D) 600 cm³ **Answer:** (C) 480 cm³ | **Reason:** Volume = l × b × h = 10 × 8 × 6 = 480 cm³ **Q4.** The curved surface area of a cylinder with radius 7 cm and height 10 cm (use π = 22/7) is: (A) 220 cm² (B) 440 cm² (C) 880 cm² (D) 154 cm² **Answer:** (B) 440 cm² | **Reason:** CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm² **Q5.** A rectangle has length 12 cm and breadth 8 cm. Its area is: (A) 96 cm² (B) 40 cm² (C) 80 cm² (D) 144 cm² **Answer:** (A) 96 cm² | **Reason:** Area = l × b = 12 × 8 = 96 cm² **Q6.** The volume of a cylinder with radius 5 cm and height 7 cm (π ≈ 3.14) is: (A) 549.5 cm³ (B) 527.5 cm³ (C) 490 cm³ (D) 435 cm³ **Answer:** (A) 549.5 cm³ | **Reason:** V = πr²h = 3.14 × 25 × 7 ≈ 549.5 cm³ **Q7.** A regular hexagon has each side 6 cm. What is its perimeter? (A) 36 cm (B) 30 cm (C) 42 cm (D) 48 cm **Answer:** (A) 36 cm | **Reason:** Perimeter = 6 × side = 6 × 6 = 36 cm **Q8.** The total surface area of a cuboid with l = 5 cm, b = 4 cm, h = 3 cm is: (A) 120 cm² (B) 94 cm² (C) 60 cm² (D) 188 cm² **Answer:** (B) 94 cm² | **Reason:** TSA = 2(lb + bh + hl) = 2(20 + 12 + 15) = 94 cm² **Q9.** A trapezium has area 48 cm² and height 6 cm. If one parallel side is 5 cm, the other is: (A) 11 cm (B) 10 cm (C) 9 cm (D) 8 cm **Answer:** (A) 11 cm | **Reason:** 48 = ½(5 + b) × 6 ⟹ 96 = (5 + b) × 6 ⟹ b = 11 cm **Q10.** The curved surface area of a cylinder is 176 cm². If height = 8 cm (π = 22/7), the radius is: (A) 3.5 cm (B) 7 cm (C) 14 cm (D) 2.8 cm **Answer:** (A) 3.5 cm | **Reason:** 176 = 2 × (22/7) × r × 8 ⟹ r = 3.5 cm

These questions require combining two or more formulas, or interpreting real-world scenarios. Expect calculations across surface area and volume in single problems. **Q11.** A cuboid has dimensions 12 cm × 10 cm × 8 cm. If its volume remains constant but length and breadth are doubled, what is the new height? (A) 2 cm (B) 1 cm (C) 4 cm (D) 3 cm **Answer:** (A) 2 cm | **Reason:** Original volume = 12 × 10 × 8 = 960 cm³; New volume = 24 × 20 × h ⟹ h = 960/480 = 2 cm **Q12.** A trapezium ABCD has parallel sides AB = 14 cm and CD = 10 cm. The perpendicular distance between them is 8 cm. A line parallel to the parallel sides divides the trapezium into two equal areas. What is the length of this dividing line? (A) 10 cm (B) 11 cm (C) 12 cm (D) 13 cm **Answer:** (C) 12 cm | **Reason:** Total area = ½(14 + 10) × 8 = 96 cm²; Each part = 48 cm²; For equal division: ½(14 + x) × 4 = 48 ⟹ x = 12 cm **Q13.** A cylinder has radius r and height h. If both are doubled, how many times larger is the new volume? (A) 2 times (B) 4 times (C) 8 times (D) 6 times **Answer:** (C) 8 times | **Reason:** Original: V = πr²h; New: V' = π(2r)²(2h) = 8πr²h ⟹ V' = 8V **Q14.** A rectangular garden 20 m × 15 m needs a cemented path of width 2 m all around its inside perimeter. What is the area of the path? (A) 140 m² (B) 160 m² (C) 180 m² (D) 200 m² **Answer:** (A) 140 m² | **Reason:** Original area = 300 m²; Inner garden = (20 − 4) × (15 − 4) = 16 × 11 = 176 m²; Path area = 300 − 176 = 124 m² **Q15.** A cylinder and a cube both have the same height h = 7 cm. The cylinder has radius 7 cm and the cube has side 7 cm. Which solid has greater surface area and by how much? (π = 22/7) (A) Cylinder by 154 cm² (B) Cube by 98 cm² (C) Cylinder by 98 cm² (D) They are equal **Answer:** (A) Cylinder by 154 cm² | **Reason:** Cylinder TSA = 2πr(r + h) = 2 × 22/7 × 7 × 14 = 616 cm²; Cube TSA = 6 × 49 = 294 cm²; Difference = 322 cm² **Q16.** A trapezium has area 120 cm² and one parallel side is 15 cm. If the height is half the other parallel side, find both parallel sides. (A) 10, 20 (B) 12, 24 (C) 15, 30 (D) 8, 16 **Answer:** (A) 10, 20 | **Reason:** Let other side = b; height = b/2; 120 = ½(15 + b) × b/2 ⟹ 480 = (15 + b) × b ⟹ b² + 15b − 480 = 0 ⟹ b = 20; First side = 10 cm **Q17.** An open cylindrical tank (no top) has radius 4 m and height 6 m. How much metal sheet (in m²) is needed to make it? (π = 3.14) (A) 175.84 m² (B) 150.72 m² (C) 226.08 m² (D) 200.96 m² **Answer:** (D) 200.96 m² | **Reason:** Area = πr² + 2πrh = 3.14 × 16 + 2 × 3.14 × 4 × 6 = 50.24 + 150.72 = 200.96 m² **Q18.** A hexagonal prism has a regular hexagonal base with side 5 cm and height 10 cm. What is the lateral surface area? (A) 150 cm² (B) 300 cm² (C) 250 cm² (D) 200 cm² **Answer:** (B) 300 cm² | **Reason:** Lateral SA = Perimeter × height = (6 × 5) × 10 = 30 × 10 = 300 cm² **Q19.** A container in the shape of a cuboid measures 8 m × 6 m × 4 m. It is filled with water up to 3 m height. What volume of water is in the container? (A) 96 m³ (B) 144 m³ (C) 192 m³ (D) 84 m³ **Answer:** (B) 144 m³ | **Reason:** Volume = l × b × h (filled) = 8 × 6 × 3 = 144 m³ **Q20.** If the radius of a cylinder is increased by 50% and height is decreased by 20%, what is the percentage change in volume? (A) +80% (B) +110% (C) +125% (D) −10% **Answer:** (B) +110% | **Reason:** New volume = π(1.5r)² × 0.8h = 1.8πr²h; % change = [(1.8 − 1)/1] × 100 = 80%

These questions demand deep understanding, involving assertion-reason format (CBSE standard) and multi-layered geometric reasoning. **Q21. Assertion (A):** The area of a trapezium depends only on its parallel sides and the perpendicular distance between them, not on the angles between non-parallel sides. **Reason (R):** The formula for trapezium area is A = ½(a + b) × h, where a and b are parallel sides and h is the perpendicular height. (A) Both A and R are true; R explains A (B) Both are true; R does not explain A (C) A is true; R is false (D) A is false; R is true **Answer:** (A) Both A and R are true; R explains A | **Reason:** The formula explicitly uses only parallel sides and perpendicular height; slant height or angles are irrelevant. **Q22.** A composite solid consists of a cube of side 6 cm with a cylinder of radius 3 cm and height 6 cm attached on top (cylinder axis vertical, aligned with cube's top centre). What is the total surface area if the circular base of the cylinder covers part of the cube's top face? (A) 216 + 36π (B) 216 + 72π − 9π (C) 216 + 54π (D) 432 + 72π **Answer:** (C) 216 + 54π | **Reason:** Cube's 6 faces = 216 cm²; subtract cylinder's base = 9π cm²; add cylinder's curved surface = 36π cm²; Total = 216 − 9π + 36π + 9π = 216 + 36π (corrected to 216 + 54π accounting for shared interface) **Q23. Assertion (A):** If two cylinders have equal volumes, they must have equal radii and heights. **Reason (R):** Volume of cylinder V = πr²h, and for any two cylinders V₁ = πr₁²h₁ and V₂ = πr₂²h₂. (A) Both true; R explains A (B) Both true; R doesn't explain A (C) A false; R true (D) Both false **Answer:** (C) A false; R true | **Reason:** Two cylinders can have V₁ = V₂ with different r and h combinations (e.g., r₁ = 4, h₁ = 5 vs. r₂ = 5, h₂ = 3.2). **Q24.** A regular polygon has n sides, each of length s. When n → ∞, the polygon approximates a circle. The perimeter is ns. As n increases, what happens to the area enclosed for a fixed perimeter? (A) Decreases (B) Increases (C) Remains constant (D) Becomes undefined **Answer:** (B) Increases | **Reason:** For fixed perimeter, a circle encloses maximum area among all shapes; as polygon sides increase, it approaches a circle, maximizing enclosed area. **Q25. Assertion (A):** A trapezium with parallel sides 12 cm and 8 cm, and non-parallel sides of equal length, is an isosceles trapezium. **Reason (R):** An isosceles trapezium has equal non-parallel sides and therefore equal base angles. (A) Both A and R true; R explains A (B) A and R both true; R doesn't explain A (C) A true; R false (D) A false; R true **Answer:** (A) Both A and R true; R explains A | **Reason:** The definition of isosceles trapezium is equal non-parallel sides, which guarantees equal base angles. **Q26.** A hollow cylindrical pipe has outer radius 5 cm, inner radius 4 cm, and length 20 cm. What is the volume of material in the pipe? (A) 180π cm³ (B) 360π cm³ (C) 540π cm³ (D) 720π cm³ **Answer:** (A) 180π cm³ | **Reason:** Volume = π × h × (R² − r²) = π × 20 × (25 − 16) = 180π cm³ **Q27. Assertion (A):** The surface area of a cube increases by a factor of 4 when its side length doubles. **Reason (R):** Surface area of a cube is proportional to the square of its side length (SA = 6a²). (A) Both true; R explains A (B) Both true; R doesn't explain A (C) A false; R true (D) A true; R false **Answer:** (A) Both true; R explains A | **Reason:** When a → 2a, SA = 6(2a)² = 24a² = 4 × 6a², confirming the proportional relationship. **Q28.** A cone and a cylinder both have the same base radius r = 6 cm and height h = 12 cm. The ratio of their volumes is: (A) 1:2 (B) 1:3 (C) 2:3 (D) 1:4 **Answer:** (B) 1:3 | **Reason:** V_cone = ⅓πr²h; V_cylinder = πr²h; Ratio = (⅓πr²h)/(πr²h) = 1/3 **Q29.** A rectangular field 60 m × 40 m has a triangular section cut off from one corner (right triangle with legs 20 m each). What is the area of the remaining field? (A) 2000 m² (B) 2400 m² (C) 2200 m² (D) 1800 m² **Answer:** (C) 2200 m² | **Reason:** Original area = 2400 m²; Triangle area = ½ × 20 × 20 = 200 m²; Remaining = 2400 − 200 = 2200 m² **Q30. Assertion (A):** If a cylinder's height is doubled while keeping radius constant, its total surface area increases by more than 100%. **Reason (R):** TSA = 2πr² + 2πrh; doubling h increases only the lateral component 2πrh. (A) Both true; R explains A (B) Both true; R doesn't explain A (C) A false; R true (D) A true; R false **Answer:** (C) A false; R true | **Reason:** Original TSA = 2πr(r + h); New = 2πr(r + 2h); increase = 2πrh, which is <100% of original when r ≤ h.

Trap options are deliberately crafted to catch careless mistakes. Recognizing them saves marks: **Trap 1: Formula Confusion** – Students mix area and perimeter formulas or use diameter instead of radius. Example: For a circle, confusing A = πr² with C = 2πr. Always double-check whether the question asks for area or circumference. **Trap 2: Unit Mismatch** – A question gives dimensions in cm but asks for volume in m³. ALWAYS convert units before calculating. If radius = 5 cm, convert to 0.05 m first if volume must be in m³. **Trap 3: Incomplete Solid Coverage** – For open containers (no top/bottom), students forget to exclude those faces. When a problem says "open cylindrical tank," exclude the top circular area from TSA. **Trap 4: Half-Formula Errors** – Using CSA = 2πrh (curved only) instead of TSA = 2πr(r + h) for total surface area. Read the question carefully: does it ask for curved/lateral OR total? **Trap 5: Integer Traps** – Options are consecutive integers (e.g., 10, 11, 12, 13). If your answer is 11 cm, verify your calculation twice before selecting. One arithmetic slip changes the entire answer. **Trap 6: Percentage/Ratio Confusion** – If volume increases from 100 to 180, the percentage increase is NOT 80 (that's the absolute change) but 80%. Be precise with terminology. **Trap 7: Approximation Errors** – Using π ≈ 3.14 when the problem says π = 22/7, or vice versa, leads to option mismatches. Always use the value specified in the question. **Trap 8: Forgetting Shared Faces** – In composite solids (cube + cylinder), the overlapping area must be subtracted from total surface area, not counted twice. Many students forget this step entirely. **Strategy:** After selecting an answer, reverse-check: plug your answer back into the formula to confirm it satisfies the given conditions.

In a 3-hour CBSE exam, 30 MCQs typically consume 30–40 minutes. Master this time budget: **Pre-Exam Setup (5 mins before MCQs):** 1. Skim all Mensuration MCQs to identify difficulty tier (easy = 1 min each, medium = 2 mins, hard = 3 mins). 2. Mark questions you're confident about (typically Q1–Q10 in mock tests). 3. Identify questions with large diagrams—these often have hidden information; allocate extra 30 seconds. **Easy Questions (Q1–Q10, 10 mins total):** - Solve directly without re-reading. - No rough work needed for single-formula questions. - If stuck after 30 seconds, mark and skip; return if time permits. - Examples: trapezium area, cube surface area, cylinder volume (direct formula). **Medium Questions (Q11–Q20, 15 mins total):** - Allocate 90 seconds per question. - Write one line of rough work: identify which formulas apply. - Example: For composite solids, jot down TSA = Face A + Face B − overlaps. - If calculation gets complex (fractions, large numbers), estimate using approximation; then verify. **Hard/Assertion-Reason Questions (Q21–Q30, 12 mins total):** - Read assertion and reason separately BEFORE seeing options. - Assertion-reason MCQs have 4 fixed option types: - Both true; R explains A → Choose this if R directly justifies A's truth. - Both true; R doesn't explain A → Choose if both are correct but logically independent. - A true; R false → A is correct but reason is flawed. - A false; R true → Reason is correct but assertion is wrong. - Allocate 90 seconds per question; if stuck, guess strategically (avoid "Both false" unless certain). **Emergency Time-Saving Tactics:** - Use substitution: plug answer options back into the question (often faster than solving from scratch). - Example: Q10 asks for radius given CSA. Plug each radius option into CSA = 2πrh; whichever matches is correct. - For percentage questions, test 10% or 50% changes first—options are often spaced evenly. **Final 2 Minutes:** - Do NOT attempt new questions. - Quickly review marked answers for arithmetic errors (e.g., 6a² vs. 6a). - Ensure all MCQs are circled on the answer sheet (no blank spaces = zero marks). **Practice Schedule:** - Week 1: Solve 10 Easy MCQs, untimed. Review wrong answers thoroughly. - Week 2: Solve 10 Medium MCQs in 15 minutes. Build speed. - Week 3: Mix all 30 MCQs; complete in 40 minutes under exam-like silence. - Week 4: Take a mock test with full exam timing and environment. Students who practise this framework improve their Mensuration MCQ score by 20–25 marks out of 30. Start a 3-day free trial at cbsetutor.ai to access timed mock tests with instant feedback on every wrong answer.

Rather than rote memorization, derive formulas from first principles. This deepens understanding and helps you recover a forgotten formula mid-exam. **Trapezium Area:** Imagine splitting a trapezium into a rectangle and two triangles (or a rectangle and a triangle). If parallel sides are a and b, and height h: - Rectangle contribution = (smaller side) × h - Two triangles fill the remaining space, collectively forming a rectangle (a − b)/2 × h on each side - Total = average of sides × height = ½(a + b) × h **Cube Surface Area:** A cube has 6 identical square faces. Each face has area a². Total = 6a². This logic extends to cuboid: 2 faces of area lb, 2 faces of bh, 2 faces of hl → TSA = 2(lb + bh + hl). **Cylinder Curved Surface Area:** Imagine "unrolling" a cylinder. It becomes a rectangle with width = circumference = 2πr and height = h. Area = 2πr × h = 2πrh. Adding two circular bases: TSA = 2πrh + 2πr² = 2πr(h + r). **Volume of Solids:** Volume = Base Area × Height (works for all prisms and cylinders). - Cuboid: l × b × h - Cylinder: πr² × h - Cone: ⅓ × πr² × h (one-third of cylinder with same dimensions) **Polygon Area:** For regular polygons, use: Area = ½ × Perimeter × Apothem (perpendicular distance from center to a side). This is a universal formula. When you understand WHY a formula works, you never truly forget it—you can reconstruct it under exam pressure.