# 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?

Result

x =  3.161 m2

#### Solution:

$h=3 \ \text{m} \ \\ r=h/2=3/2=\dfrac{ 3 }{ 2 }=1.5 \ \text{m} \ \\ q=20 \%=\dfrac{ 20 }{ 100 }=0.2 \ \\ \ \\ s=\sqrt{ h^2+r^2 }=\sqrt{ 3^2+1.5^2 } \doteq 3.3541 \ \text{m} \ \\ x=q \cdot \ \pi \cdot \ r \cdot \ s=0.2 \cdot \ 3.1416 \cdot \ 1.5 \cdot \ 3.3541 \doteq 3.1612 \doteq 3.161 \ \text{m}^2$

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