Tower roof area

The administrator of the castle is trying to estimate how many square meters of sheet metal will be needed for the new roof of the tower. The roof has the shape of a cone. The castle administrator knows that the tower's diameter is 4.6 meters and its height is 5.2 meters. How many square meters does the roof measure?

Final Answer:

S =  41.0847 m²

Step-by-step explanation:

$$\begin{gathered} D=4.6\text{m} \\ h=5.2\text{m} \\ r=D/2=4.6/2=\frac{23}{10}=2.3\text{m} \\ s=\sqrt{r^2+h^2}=\sqrt{2.3^2+5.2^2}\doteq 5.6859\text{m} \\ S=\pi \cdot r\cdot s=3.1416\cdot 2.3\cdot 5.6859=41.0847{\text{m}}^2 \end{gathered}$$

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