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CAT Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the Common Admission Test: 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 distance between (-2, 5) and (4, 13).
Show answer & explanation
Answer: A — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q2.A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
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Answer: D — 10 cm
By Pythagoras, hypotenuse = √(6² + 8²) = √100 = 10.
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Q3.Find the volume of a cylinder with radius 7 cm and height 4 cm (take π = 22/7).
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Answer: D — 616 cm³
Using πr²h with π = 22/7: 616 cm³.
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Q4.Find the distance between (-1, -5) and (4, 7).
Show answer & explanation
Answer: A — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q5.Find the distance between (3, -5) and (9, 3).
Show answer & explanation
Answer: D — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q6.Find the volume of a cone with radius 7 cm and height 7 cm (take π = 22/7).
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Answer: C — 359.33 cm³
Using ⅓πr²h with π = 22/7: 359.33 cm³.
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Q7.Find the distance between (-2, 1) and (1, 5).
Show answer & explanation
Answer: D — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q8.Find the volume of a cylinder with radius 7 cm and height 10 cm (take π = 22/7).
Show answer & explanation
Answer: C — 1,540 cm³
Using πr²h with π = 22/7: 1,540 cm³.
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Q9.Find the distance between (4, 1) and (7, 5).
Show answer & explanation
Answer: C — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q10.Find the volume of a cylinder with radius 7 cm and height 5 cm (take π = 22/7).
Show answer & explanation
Answer: D — 770 cm³
Using πr²h with π = 22/7: 770 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 CAT
Common Admission Test — conducted by Indian Institutes of Management (convening IIM rotates). The entrance exam for IIM MBA programmes, with VARC, DILR and Quantitative Ability sections.
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.
CAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Ratio, Ages & Mixtures | Quantitative aptitude | Calculated (new numbers every set) |
| Time, Work & Pipes | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |