# Hemisphere - roof

The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of paint is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of paint will paint an area of 7.3 dm2.

Result

b =  52.073 kg
r =  5.207 l

#### Solution:

$D=11 \ \text{m} \ \\ r=D/2=11/2=\dfrac{ 11 }{ 2 }=5.5 \ \text{m} \ \\ \ \\ S_{0}=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 5.5^2 \doteq 380.1327 \ \text{m}^2 \ \\ S=\dfrac{ 1 }{ 2 } \cdot \ 2 \cdot \ S_{0}=\dfrac{ 1 }{ 2 } \cdot \ 2 \cdot \ 380.1327 \doteq 380.1327 \ \text{m}^2 \ \\ \ \\ S_{1}=7.3 \ \text{m}^2 \ \\ \ \\ b=S/S_{1}=380.1327/7.3 \doteq 52.073 \doteq 52.073 \ \text{kg}$
$r_{1}=b=52.073 \ \text{dl} \ \\ r=r_{1} \rightarrow l=r_{1} / 10 \ l=5.2073 \ l=5.207 \ \text{l}$

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