Tower

How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°?

Correct answer:

S =  482 m²

Step-by-step explanation:

$$\begin{gathered} D=23\text{m} \\ \alpha =119{}^{\circ } \\ r=D/2=23/2=\frac{23}{2}=11.5\text{m} \\ \beta =\alpha /2=119/2=\frac{119}{2}=59.5{}^{\circ } \\ \sin \beta =r:s \\ s=r/\sin \beta =r/\sin 59.5°=11.5/\sin 59.5°=11.5/0.861629=13.34681\text{m} \\ S=\pi \cdot r\cdot s=3.1416\cdot 11.5\cdot 13.3468=482{\text{m}}^2 \end{gathered}$$

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