Storm and roof

The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m² of roof need to be repaired if 20% were damaged in a storm?

Correct result:

x =  3.1612 m²

Solution:

$$\begin{gathered} h=3\text{ m } \\ r=h\mathrm{/}2=3\mathrm{/}2={\displaystyle \frac{3}{2}}=1.5\text{ m } \\ q=20\mathrm{\%}={\displaystyle \frac{20}{100}}=0.2 \\ s=\sqrt{h^2+r^2}=\sqrt{3^2+1.5^2}\doteq 3.3541\text{ m } \\ x=q\cdot \pi \cdot r\cdot s=0.2\cdot 3.1416\cdot 1.5\cdot 3.3541=3.1612{\text{m}}^2 \end{gathered}$$

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