Cone roof cost

The roof of the castle tower has the shape of a cone with a base diameter of 12 m and a height of 8 m. How many euros will we pay to cover the roof if 1m of square roofing costs 3.5 euros?

Final Answer:

x =  659.7345 Eur

Step-by-step explanation:

$$\begin{gathered} D=12\text{m} \\ h=8\text{m} \\ c=3.5{\text{Eur/m}}^2 \\ r=D/2=12/2=6\text{m} \\ s=\sqrt{r^2+h^2}=\sqrt{6^2+8^2}=10\text{m} \\ S=\pi \cdot r\cdot s=3.1416\cdot 6\cdot 10\doteq 188.4956{\text{m}}^2 \\ x=S\cdot c=188.4956\cdot 3.5=659.7345\text{Eur} \end{gathered}$$

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