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 thinner is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of thinner will paint an area of 7.3 m².

Correct result:

b =  52.073 kg
r =  5.2073 l

Solution:

$$\begin{gathered} D=11\text{ m } \\ r=D\mathrm{/}2=11\mathrm{/}2={\displaystyle \frac{11}{2}}=5{\displaystyle \frac{1}{2}}=5.5\text{ m } \\ {S}_0=4\pi \cdot r^2=4\cdot 3.1416\cdot 5.5^2\doteq 380.1327{\text{m}}^2 \\ S={\displaystyle \frac{1}{2}}\cdot 2\cdot S_0={\displaystyle \frac{1}{2}}\cdot 2\cdot 380.1327\doteq 380.1327{\text{m}}^2 \\ {S}_1=7.3{\text{m}}^2 \\ b=S\mathrm{/}{S}_1=380.1327\mathrm{/}7.3=52.073\text{ kg} \end{gathered}$$

$$\begin{gathered} r_1=b=52.073\doteq 52.073\text{ dl } \\ r=r_1\to \text{ l}=r_1\mathrm{/}10\text{ l}=52.073\mathrm{/}10\text{ l}=5.207\text{ l}=5.2073\text{ l} \end{gathered}$$

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