0580/21 May/Jun 2022, Question 11: Similar Triangles
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks
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The question, in short
Using similar triangles ABC and PQR, with AB = 8 cm, BC = 6 cm and PQ = 6 cm, find a missing side and then a prism volume.
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Part (a) · 2 marks
Work out the length QR using the scale factor between the two similar triangles.
- 1PQ matches AB, so scale factor = 6 ÷ 8 = 0.75
- 2QR matches BC: QR = 6 × 0.75
- 3QR = 4.5 cm
Answer4.5
Part (b) · 2 marks
Given the larger prism volume is 320 cm³, work out the smaller prism's volume from the triangles' scale factor.
- 1Length scale factor (small ÷ large) = 6/8 = 3/4
- 2Volume scale factor = (3/4)³ = 27/64
- 3Volume = 320 × 27/64 = 135 cm³
Answer135
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Also searched as: 0580/21/M/J/22 · 0580_s22_qp_21 · 0580 s22 21 · question 11.
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