0580/43 Oct/Nov 2022, Question 5: Trigonometry in 3D: Cuboids

Part (a) · 3 marks

Show the trough's capacity equals 206.4 litres using the trapezium cross-section and 1.2 m length.

1. 1Cross-section = (36 + 50)/2 × 40 = 1720 cm²
2. 2Volume = 1720 × 120 = 206400 cm³
3. 3206400 ÷ 1000 = 206.4 litres

Answer206.4

Part (b) · 3 marks

Calculate emptying time in minutes and seconds at a 600 ml per second flow rate.

1. 1Cross-section area = (50 + 36)/2 × 40 = 1720 cm²
2. 2Volume = 1720 × 120 = 206400 cm³ = 206400 ml
3. 3Time = 206400 ÷ 600 = 344 seconds
4. 4344 s = 5 × 60 + 44, so 5 minutes 44 seconds

Answer5 minutes 44 seconds

Part (ci) · 3 marks

Calculate the tank radius from the water volume and 84 cm depth.

1. 1π × r² × 84 = 206400
2. 2r² = 206400 ÷ (84π) = 782.13…
3. 3r = 27.96… ≈ 28.0 cm

Answer28.0 or 27.96 to 27.97

Part (cii) · 2 marks

Calculate the tank's full height given it is 60% full at 84 cm depth.

1. 10.6h = 84
2. 2h = 84 ÷ 0.6 = 140 cm

Answer140

Part (d) · 4 marks

Calculate steel rod AM from a base vertex to the midpoint of the opposite top edge.

1. 1M is above the middle of the base, so horizontal distance across = 36 ÷ 2 = 18 cm
2. 2AM² = 18² + 120² + 40² = 324 + 14400 + 1600 = 16324
3. 3AM = √16324 = 127.76… ≈ 128 cm

Answer128 or 127.7 to 127.8

More past-paper questions on trigonometry in 3d: cuboids

• 0580/21 May/Jun 2026 Q21 · 9 marks
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