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CAT Geometry & Mensuration — practice questions

Explore 9 free Geometry & Mensuration questions in CAT Quantitative Reasoning. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry & Mensuration questions and exercises with answers

Showing questions 1–9 of 9.

A right triangle has legs 6 and 8. The length of the hypotenuse is:Read the answer and worked solution →A cube's side doubles. By what factor does its VOLUME grow?Read the answer and worked solution →The area of a circle of radius 7 cm (using π = 22/7) is:Read the answer and worked solution →A cylindrical water tank has radius 7 m and height 5 m. Its volume (using π = 22/7) is:Read the answer and worked solution →A cone has radius 3 and height 4. Its slant height is:Read the answer and worked solution →The sum of the interior angles of a hexagon is:Read the answer and worked solution →Three rope pieces have lengths 4, 6 and 11 metres. Can they form a triangle?Read the answer and worked solution →In a 30-60-90 right triangle, the side opposite the 30° angle has length 5. The side opposite the 60° angle has length:Read the answer and worked solution →A triangle has sides 5, 12 and 13. The radius of its inscribed circle (inradius) is:Read the answer and worked solution →

Worked practice questions

A right triangle has legs 6 and 8. The length of the hypotenuse is:

  1. $12$
  2. $10$
  3. $14$
  4. $48$
Show answer and solution

Correct answer: B. $10$

By Pythagoras: hypotenuse² = 6² + 8² = 36 + 64 = 100. Hypotenuse = 10. This is the 6-8-10 triple (3-4-5 doubled).

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A cube's side doubles. By what factor does its VOLUME grow?

  1. $2$
  2. $3$
  3. $4$
  4. $8$
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Correct answer: D. $8$

Volume scales with the cube of the linear factor. (2)³ = 8.

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The area of a circle of radius 7 cm (using π = 22/7) is:

  1. $154$ cm
  2. $22$ cm
  3. $154$ cm²
  4. $44$ cm²
Show answer and solution

Correct answer: C. $154$ cm²

Area = πr² = (22/7) × 49 = 22 × 7 = 154 cm².

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