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ISEE Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the Independent School Entrance Exam: 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 (0, -3) and (8, 12).
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Answer: B — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q2.Find the volume of a cone with radius 2 cm and height 20 cm.
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Answer: C — 83.78 cm³
Using ⅓πr²h with π = 3.1416: 83.78 cm³.
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Q3.Find the area of a right triangle with legs 3 cm and 4 cm.
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Answer: B — 6 cm²
Area = ½ × base × height = ½ × 3 × 4 = 6 cm².
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Q4.A right triangle has legs 7 cm and 24 cm. Find the hypotenuse.
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Answer: A — 25 cm
By Pythagoras, hypotenuse = √(7² + 24²) = √625 = 25.
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Q5.A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
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Answer: B — 10 cm
By Pythagoras, hypotenuse = √(6² + 8²) = √100 = 10.
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Q6.A right triangle has legs 5 cm and 12 cm. Find the hypotenuse.
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Answer: C — 13 cm
By Pythagoras, hypotenuse = √(5² + 12²) = √169 = 13.
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Q7.A right triangle has legs 3 cm and 4 cm. Find the hypotenuse.
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Answer: A — 5 cm
By Pythagoras, hypotenuse = √(3² + 4²) = √25 = 5.
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Q8.Find the volume of a sphere of radius 6 cm.
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Answer: B — 904.78 cm³
Using (4/3)πr³ with π = 3.1416: 904.78 cm³.
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Q9.Find the volume of a cone with radius 9 cm and height 8 cm.
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Answer: B — 678.58 cm³
Using ⅓πr²h with π = 3.1416: 678.58 cm³.
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Q10.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.
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 ISEE
Independent School Entrance Exam — conducted by Educational Records Bureau (ERB). Admission test for independent schools with verbal and quantitative reasoning 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.
ISEE practice topics
| Topic | Section | Question source |
|---|---|---|
| Vocabulary & Idioms | English | Question bank |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |