Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.

Correct result:

S =  197.5848 m²

Solution:

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

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