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SAT Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the SAT (Digital): 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 cone with radius 3 cm and height 20 cm.
Show answer & explanation
Answer: C — 188.5 cm³
Using ⅓πr²h with π = 3.1416: 188.5 cm³.
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Q2.Find the area of a right triangle with legs 6 cm and 8 cm.
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Answer: A — 24 cm²
Area = ½ × base × height = ½ × 6 × 8 = 24 cm².
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Q3.Find the distance between (-3, -4) and (5, 11).
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Answer: C — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q4.Find the area of a right triangle with legs 9 cm and 12 cm.
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Answer: D — 54 cm²
Area = ½ × base × height = ½ × 9 × 12 = 54 cm².
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Q5.Find the volume of a cone with radius 9 cm and height 6 cm.
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Answer: B — 508.94 cm³
Using ⅓πr²h with π = 3.1416: 508.94 cm³.
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Q6.Find the volume of a cylinder with radius 6 cm and height 15 cm.
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Answer: A — 1,696.46 cm³
Using πr²h with π = 3.1416: 1,696.46 cm³.
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Q7.Find the area of a circle of radius 4 cm.
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Answer: A — 50.27 cm²
Using πr² with π = 3.1416: 50.27 cm².
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Q8.Find the area of a right triangle with legs 3 cm and 4 cm.
Show answer & explanation
Answer: A — 6 cm²
Area = ½ × base × height = ½ × 3 × 4 = 6 cm².
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Q9.Find the area of a right triangle with legs 7 cm and 24 cm.
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Answer: B — 84 cm²
Area = ½ × base × height = ½ × 7 × 24 = 84 cm².
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Q10.Find the volume of a sphere of radius 6 cm.
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Answer: C — 904.78 cm³
Using (4/3)πr³ with π = 3.1416: 904.78 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 SAT
SAT (Digital) — conducted by College Board. The US college admission test with Reading & Writing and Math sections, now delivered digitally.
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.
SAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Averages & Statistics | Quantitative aptitude | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| Vocabulary & Idioms | English | Question bank |