# 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:

$D=10 \ \text{m} \ \\ h=4 \ \text{m} \ \\ q=4 \%=1 + \dfrac{ 4 }{ 100 }=1.04 \ \\ \ \\ r=D/2=10/2=5 \ \text{m} \ \\ s=\sqrt{ h^2+r^2 }=\sqrt{ 4^2+5^2 } \doteq \sqrt{ 41 } \ \text{m} \doteq 6.4031 \ \text{m} \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 5 \cdot \ 6.4031 \doteq 100.58 \ \text{m}^2 \ \\ \ \\ S=q \cdot \ S_{1}=1.04 \cdot \ 100.58 \doteq 104.6032 \doteq 104.603 \ \text{m}^2$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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