0580/22 Feb/Mar 2021, Question 20: Volume Factor of Similar Shapes
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 5 marks
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The question, in short
Use similar triangles and similar solids to find an unknown side and a bowl height from given lengths and capacities.
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Part (a) · 2 marks
Find x using the side lengths of two mathematically similar triangles, with AC = 1.61 cm, CB = 2.8 cm, PR = x cm and RQ = 3.2 cm.
- 1Corresponding sides: x/1.61 = 3.2/2.8
- 2x = 1.61 × 3.2 ÷ 2.8
- 3x = 1.84
Answer1.84
Part (b) · 3 marks
Calculate the height of the smaller bowl given the larger bowl's capacity 7.8 litres and height 11.5 cm, and the smaller capacity 4 litres.
- 1Volume scale factor = 4/7.8
- 2Length scale factor = ∛(4/7.8) = 0.8004…
- 3Height = 11.5 × ∛(4/7.8) = 9.204…
- 4≈ 9.20 cm
Answer9.20 or 9.204 to 9.205
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Also searched as: 0580/22/F/M/21 · 0580_m21_qp_22 · 0580 m21 22 · question 20.
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