0580/42 May/Jun 2021, Question 8: Nets of 3D Shapes
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 14 marks
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The question, in short
Use the cuboid net dimensions and the ratio W:L = 1:2 to find L, W and H; then for a pyramid with given base and edge lengths, find the wood density and the angle between BE and the base.
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Part (a) · 5 marks
Using the net's overall width 37.8 cm and height 20.1 cm with W:L = 1:2, find the values of L, W and H.
- 1From the net: L = 2W, W + 2H = 20.1, 2L + 2H = 37.8
- 2Substitute L = 2W: 4W + 2H = 37.8
- 3Subtract W + 2H = 20.1: 3W = 17.7, W = 5.9
- 4L = 2 × 5.9 = 11.8, 2H = 20.1 − 5.9 = 14.2, H = 7.1
- 5L = 11.8, W = 5.9, H = 7.1
AnswerL = 11.8, W = 5.9, H = 7.1
Part (bi) · 5 marks
Given the pyramid's dimensions and mass 800 g, calculate the wood's density using V = 1/3 × base area × height, and state its units.
- 1DC = AB = 18, so ED = √(24² − 18²) = √252 = 15.87… cm
- 2Volume = 1/3 × 18 × 15 × 15.87… = 1428.7… cm³
- 3Density = 800 ÷ 1428.7… = 0.5599… g/cm³ ≈ 0.560 g/cm³
Answer0.559 to 0.560 g/cm³
Part (bii) · 4 marks
Calculate the angle that the line BE makes with the rectangular base of the pyramid.
- 1The angle is EBD; BD = √(18² + 15²) = √549 = 23.43… cm
- 2tan EBD = √252 ÷ √549 = 15.87… ÷ 23.43…
- 3Angle EBD = 34.11… ≈ 34.1°
Answer34.1 or 34.11 to 34.12
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Also searched as: 0580/42/M/J/21 · 0580_s21_qp_42 · 0580 s21 42 · question 8.
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