Half-sphere roof

The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is this roof's cost if the cost of 1 square meter is 12 euros and 40 cents?

Correct answer:

x =  2994.92 Eur

Step-by-step explanation:

$$\begin{gathered} D=12.4\text{m} \\ r=D/2=12.4/2=\frac{31}{5}=6.2 \\ S=\frac{1}{2}\cdot 4\pi \cdot r^2=\frac{1}{2}\cdot 4\cdot 3.1416\cdot 6.2^2\doteq 241.5256{\text{m}}^2 \\ x=12.40\cdot S=12.40\cdot 241.5256=2994.92\text{Eur} \end{gathered}$$

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