Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. If we add one-third to the overlap, calculate how many m² of coverage is needed to cover it.

Correct answer:

S =  197.5848 m²

Step-by-step explanation:

$$\begin{gathered} D=10\text{m} \\ h=8\text{m} \\ r=D/2=10/2=5\text{m} \\ s=\sqrt{h^2+r^2}=\sqrt{8^2+5^2}=\sqrt{89}\text{m}\doteq 9.434\text{m} \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 5\cdot 9.434\doteq 148.1886{\text{m}}^2 \\ S=(1+\frac{1}{3})\cdot S_1=(1+\frac{1}{3})\cdot 148.1886=197.5848{\text{m}}^2 \end{gathered}$$

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