How many

How many m² of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters, if we count 8% of the material for bending and waste?

Correct result:

S =  548.3641 m²

Solution:

$$\begin{gathered} D=13\text{ m } \\ h=24\text{ m } \\ q=8\mathrm{\%}=1+{\displaystyle \frac{8}{100}}=1.08 \\ r=D\mathrm{/}2=13\mathrm{/}2={\displaystyle \frac{13}{2}}=6.5\text{ m } \\ s=\sqrt{h^2+r^2}=\sqrt{24^2+6.5^2}\doteq 24.8646\text{ m } \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 6.5\cdot 24.8646\doteq 507.7446{\text{m}}^2 \\ S=q\cdot S_1=1.08\cdot 507.7446=548.3641{\text{m}}^2 \end{gathered}$$

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