# Half-sphere roof

The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is the cost of this roof, if the cost of 1 square meter is 12 euros and 40 cents?

Result

x =  2994.92 Eur

#### Solution:

$D=12.4 \ \text{m} \ \\ r=D/2=12.4/2=\dfrac{ 31 }{ 5 }=6.2 \ \\ \ \\ S=\dfrac{ 1 }{ 2 } \cdot \ 4 \pi \cdot \ r^2=\dfrac{ 1 }{ 2 } \cdot \ 4 \cdot \ 3.1416 \cdot \ 6.2^2 \doteq 241.5256 \ \text{m}^2 \ \\ \ \\ x=12.40 \cdot \ S=12.40 \cdot \ 241.5256 \doteq 2994.918 \doteq 2994.92 \ \text{Eur}$

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