Cone roof

How many m² of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.

Correct answer:

S =  104.6032 m²

Step-by-step explanation:

$$\begin{gathered} D=10\text{ m } \\ h=4\text{ m } \\ q=4\mathrm{\%}=1+{\displaystyle \frac{4}{100}}=1.04 \\ r=D\mathrm{/}2=10\mathrm{/}2=5\text{ m } \\ s=\sqrt{h^2+r^2}=\sqrt{4^2+5^2}=\sqrt{41}\text{ m}\doteq 6.4031\text{ m } \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 5\cdot 6.4031\doteq 100.58{\text{m}}^2 \\ S=q\cdot S_1=1.04\cdot 100.58=104.6032{\text{m}}^2 \end{gathered}$$

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