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UPSC CDS Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the Combined Defence Services Examination: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Geometry & Mensuration practice
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Q1.Find the volume of a sphere of radius 14 cm (take π = 22/7).
Show answer & explanation
Answer: B — 11,498.67 cm³
Using (4/3)πr³ with π = 22/7: 11,498.67 cm³.
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Q2.A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
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Answer: C — 15 cm
By Pythagoras, hypotenuse = √(9² + 12²) = √225 = 15.
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Q3.Find the volume of a sphere of radius 3.5 cm (take π = 22/7).
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Answer: A — 179.67 cm³
Using (4/3)πr³ with π = 22/7: 179.67 cm³.
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Q4.Find the volume of a cone with radius 3.5 cm and height 17 cm (take π = 22/7).
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Answer: A — 218.17 cm³
Using ⅓πr²h with π = 22/7: 218.17 cm³.
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Q5.A right triangle has legs 20 cm and 21 cm. Find the hypotenuse.
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Answer: C — 29 cm
By Pythagoras, hypotenuse = √(20² + 21²) = √841 = 29.
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Q6.Find the area of a right triangle with legs 9 cm and 12 cm.
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Answer: B — 54 cm²
Area = ½ × base × height = ½ × 9 × 12 = 54 cm².
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Q7.Find the volume of a cone with radius 14 cm and height 5 cm (take π = 22/7).
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Answer: B — 1,026.67 cm³
Using ⅓πr²h with π = 22/7: 1,026.67 cm³.
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Q8.Find the distance between (1, -4) and (7, 4).
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Answer: B — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q9.Find the distance between (-4, 2) and (1, 14).
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Answer: C — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q10.Find the volume of a cone with radius 21 cm and height 16 cm (take π = 22/7).
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Answer: D — 7,392 cm³
Using ⅓πr²h with π = 22/7: 7,392 cm³.
How to approach geometry & mensuration questions
Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)). Sketch the figure — most errors come from misreading which length is given.
About UPSC CDS
Combined Defence Services Examination — conducted by Union Public Service Commission (UPSC). Selects officers for the Indian Military Academy, Naval Academy, Air Force Academy and Officers’ Training Academy.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
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