Cross-section 62964

The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg.

Correct answer:

x = 14809.03 Eur
m = 2358.5 kg

Step-by-step explanation:

a = 8 m b = 5 m α = 30^{\circ} tan α = h : (a / 2) h_{1} = \frac{a}{2} \cdot tan α = \frac{a}{2} \cdot tan 30 ° = \frac{8}{2} \cdot tan 30 ° = \frac{8}{2} \cdot 0.57735 = 2.3094 m h_{2} = \frac{b}{2} \cdot tan α = \frac{b}{2} \cdot tan 30 ° = \frac{5}{2} \cdot tan 30 ° = \frac{5}{2} \cdot 0.57735 = 1.44338 m h = min (h_{1}, h_{2}) = min (2.3094, 1.4434) ≐ 1.4434 m sin α = h : s s = h / sin α = h / sin 30 ° = 1.4434 / sin 30 ° = 1.4434 / 0.5 = 2.88675 m w = s^{2} - h^{2} = 2.886 8^{2} - 1.443 4^{2} = \frac{5}{2} = 2.5 m c = a - 2 \cdot w = 8 - 2 \cdot \frac{5}{2} = 3 m S_{1} = \frac{a \cdot s}{2} = \frac{8 \cdot 2 . 8 8 6 8}{2} ≐ 11.547 m^{2} S_{2} = \frac{a + c}{2} \cdot s = \frac{8 + 3}{2} \cdot 2.8868 ≐ 15.8771 m^{2} S = 2 \cdot S_{1} + 2 \cdot S_{2} = 2 \cdot 11.547 + 2 \cdot 15.8771 ≐ 54.8483 m^{2} x = 270 \cdot S = 270 \cdot 54.8483 = 14809.03 Eur

ρ = 43 kg/m^{2} m = ρ \cdot S = 43 \cdot 54.8483 = 2358.5 kg

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