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.

Result

S =  104.603 m2

Solution:

$D=10 \ \text{m} \ \\ h=4 \ \text{m} \ \\ q=4 \%=1 + \dfrac{ 4 }{ 100 }=1.04 \ \\ \ \\ r=D/2=10/2=5 \ \text{m} \ \\ s=\sqrt{ h^2+r^2 }=\sqrt{ 4^2+5^2 } \doteq \sqrt{ 41 } \ \text{m} \doteq 6.4031 \ \text{m} \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 5 \cdot \ 6.4031 \doteq 100.58 \ \text{m}^2 \ \\ \ \\ S=q \cdot \ S_{1}=1.04 \cdot \ 100.58 \doteq 104.6032 \doteq 104.603 \ \text{m}^2$

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