Half-sphere roof

The roof above the castle tower has the shape of a 16 m diameter half-sphere. What is this roof's cost if the cost of 1 square meter is 12 euros and 40 cents?

Final Answer:

x =  4986.34 Eur

Step-by-step explanation:

$$\begin{gathered} D=16\text{m} \\ r=D/2=16/2=8\text{m} \\ S=\frac{1}{2}\cdot 4\pi \cdot r^2 \\ S=2\pi \cdot r^2=2\cdot 3.1416\cdot 8^2\doteq 402.1239{\text{m}}^2 \\ x=12.40\cdot S=12.40\cdot 402.1239=4986.34\text{Eur} \end{gathered}$$

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