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DAT Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the Dental Admission Test: 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 (5, 5) and (13, 20).
Show answer & explanation
Answer: B — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q2.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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Q3.Find the volume of a cone with radius 9 cm and height 8 cm.
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Answer: C — 678.58 cm³
Using ⅓πr²h with π = 3.1416: 678.58 cm³.
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Q4.Find the volume of a cylinder with radius 9 cm and height 20 cm.
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Answer: D — 5,089.38 cm³
Using πr²h with π = 3.1416: 5,089.38 cm³.
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Q5.A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
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Answer: A — 15 cm
By Pythagoras, hypotenuse = √(9² + 12²) = √225 = 15.
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Q6.Find the area of a right triangle with legs 20 cm and 21 cm.
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Answer: A — 210 cm²
Area = ½ × base × height = ½ × 20 × 21 = 210 cm².
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Q7.Find the distance between (-5, 5) and (3, 20).
Show answer & explanation
Answer: B — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q8.Find the volume of a cone with radius 3 cm and height 5 cm.
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Answer: A — 47.12 cm³
Using ⅓πr²h with π = 3.1416: 47.12 cm³.
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Q9.Find the volume of a sphere of radius 8 cm.
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Answer: C — 2,144.66 cm³
Using (4/3)πr³ with π = 3.1416: 2,144.66 cm³.
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Q10.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.
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 DAT
Dental Admission Test — conducted by American Dental Association (ADA). Dental school admission test covering natural sciences, perceptual ability, reading and quantitative reasoning.
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.
DAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Biology | Science | Question bank |
| Chemistry | Science | Calculated + question bank |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |