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EJU Mathematics Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the Examination for Japanese University Admission — Mathematics: 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 area of a right triangle with legs 5 cm and 12 cm.
Show answer & explanation
Answer: D — 30 cm²
Area = ½ × base × height = ½ × 5 × 12 = 30 cm².
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Q2.Find the distance between (-4, 4) and (-1, 8).
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Answer: D — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q3.Find the volume of a cylinder with radius 5 cm and height 3 cm.
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Answer: D — 235.62 cm³
Using πr²h with π = 3.1416: 235.62 cm³.
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Q4.A right triangle has legs 20 cm and 21 cm. Find the hypotenuse.
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Answer: B — 29 cm
By Pythagoras, hypotenuse = √(20² + 21²) = √841 = 29.
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Q5.Find the distance between (3, -2) and (9, 6).
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Answer: D — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q6.Find the volume of a cylinder with radius 7 cm and height 8 cm.
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Answer: C — 1,231.5 cm³
Using πr²h with π = 3.1416: 1,231.5 cm³.
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Q7.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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Q8.Find the area of a right triangle with legs 6 cm and 8 cm.
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Answer: D — 24 cm²
Area = ½ × base × height = ½ × 6 × 8 = 24 cm².
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Q9.A right triangle has legs 3 cm and 4 cm. Find the hypotenuse.
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Answer: C — 5 cm
By Pythagoras, hypotenuse = √(3² + 4²) = √25 = 5.
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Q10.Find the distance between (-5, -2) and (-2, 2).
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Answer: A — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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 EJU Mathematics
Examination for Japanese University Admission — Mathematics — conducted by Japan Student Services Organization (JASSO). Taken by international students applying to Japanese universities.
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.
EJU Mathematics practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |