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Gaokao-style Maths Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the Gaokao-style Mathematics practice: 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 5 cm.
Show answer & explanation
Answer: B — 523.6 cm³
Using (4/3)πr³ with π = 3.1416: 523.6 cm³.
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Q2.Find the area of a right triangle with legs 7 cm and 24 cm.
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Answer: D — 84 cm²
Area = ½ × base × height = ½ × 7 × 24 = 84 cm².
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Q3.A right triangle has legs 5 cm and 12 cm. Find the hypotenuse.
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Answer: B — 13 cm
By Pythagoras, hypotenuse = √(5² + 12²) = √169 = 13.
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Q4.Find the volume of a sphere of radius 8 cm.
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Answer: A — 2,144.66 cm³
Using (4/3)πr³ with π = 3.1416: 2,144.66 cm³.
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Q5.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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Q6.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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Q7.Find the distance between (-1, 2) and (2, 6).
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Answer: C — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q8.Find the distance between (-1, 4) and (4, 16).
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Answer: A — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q9.Find the distance between (-4, 1) and (2, 9).
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Answer: B — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q10.Find the area of a circle of radius 3 cm.
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Answer: C — 28.27 cm²
Using πr² with π = 3.1416: 28.27 cm².
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 Gaokao-style Maths
Gaokao-style Mathematics practice — conducted by Practice in the style of China’s National College Entrance Examination; not affiliated. Practice in the style of the maths paper of China’s university entrance exam: functions, sequences, probability and geometry.
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.
Gaokao-style Maths 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) |