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4024/11 Oct/Nov 2025, Question 17: Volume of a Prism

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Use the isosceles triangle cross-section with sides 13 cm and base 10 cm, and prism length 3 cm, to prove the volume is 180 cm³, then find base x of a similar prism with volume 1440 cm³.

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Part (a) · 4 marks

Show the prism volume equals 180 cm³ using the isosceles triangle cross-section (sides 13 cm, base 10 cm) and length 3 cm.

  1. 1Height of triangle: h² + 5² = 13²
  2. 2h = √(169 − 25) = √144 = 12 cm
  3. 3Area of cross-section = 1/2 × 10 × 12 = 60 cm²
  4. 4Volume = 60 × 3 = 180 cm³

Answerheight = 12; 1/2 × 10 × √(13² − 5²) × 3 leading to 180

Part (b) · 3 marks

For a similar prism of volume 1440 cm³, calculate the base x cm of its isosceles triangle cross-section.

  1. 1Volume scale factor = 1440 ÷ 180 = 8
  2. 2Length scale factor = ∛8 = 2
  3. 3x = 10 × 2 = 20

Answer20

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Also searched as: 4024/11/O/N/25 · 4024_w25_qp_11 · 4024 w25 11 · question 17.
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