Cone roof consumption

The roof of a tower has the shape of a lateral surface of a cone with a base diameter of 4.3 m. The angle between the slant side and the base plane is 36°. Calculate the amount of sheet metal needed to cover the roof, allowing 8% for waste.

Final Answer:

S =  19.39 m²

Step-by-step explanation:

$$\begin{gathered} d=4.3\text{m} \\ \alpha =36°\to \text{rad}=36°\cdot \frac{\pi }{180}=36°\cdot \frac{3.1415926}{180}=0.62832=\pi /5 \\ q=100\%+8\%=1+\frac{8}{100}=1.08 \\ r=d/2=4.3/2=\frac{43}{20}=2.15\text{m} \\ \cos \alpha =r:s \\ s=r/\cos \alpha =2.15/\cos 0.6283\doteq 2.6575\text{m} \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 2.15\cdot 2.6575\doteq 17.9502 \\ S=q\cdot S_1=1.08\cdot 17.9502=19.39{\text{m}}^2 \end{gathered}$$

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