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ACT Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the ACT: 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 circle of radius 2 cm.
Show answer & explanation
Answer: B — 12.57 cm²
Using πr² with π = 3.1416: 12.57 cm².
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Q2.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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Q3.Find the distance between (0, 4) and (8, 19).
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Answer: B — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q4.Find the volume of a cone with radius 6 cm and height 3 cm.
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Answer: C — 113.1 cm³
Using ⅓πr²h with π = 3.1416: 113.1 cm³.
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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.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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Q7.Find the distance between (3, -4) and (11, 11).
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Answer: B — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q8.A right triangle has legs 3 cm and 4 cm. Find the hypotenuse.
Show answer & explanation
Answer: C — 5 cm
By Pythagoras, hypotenuse = √(3² + 4²) = √25 = 5.
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Q9.Find the distance between (3, -1) and (6, 3).
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Answer: D — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q10.Find the volume of a cone with radius 7 cm and height 10 cm.
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Answer: D — 513.13 cm³
Using ⅓πr²h with π = 3.1416: 513.13 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 ACT
ACT — conducted by ACT, Inc.. US college admission test with English, Math and Reading, plus an optional Science section.
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.
ACT practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |