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 =  197.585 m2

Solution:

$D=10 \ \text{m} \ \\ h=8 \ \text{m} \ \\ \ \\ r=D/2=10/2=5 \ \text{m} \ \\ \ \\ s=\sqrt{ h^2 + r^2 }=\sqrt{ 8^2 + 5^2 } \doteq \sqrt{ 89 } \ \text{m} \doteq 9.434 \ \text{m} \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 5 \cdot \ 9.434 \doteq 148.1886 \ \text{m}^2 \ \\ \ \\ S=(1+\dfrac{ 1 }{ 3 } ) \cdot \ S_{1}=(1+\dfrac{ 1 }{ 3 } ) \cdot \ 148.1886=197.585 \ \text{m}^2$

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