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 are 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 answer:

b =  52.073 kg
r =  5.2073 l

Step-by-step explanation:

$$\begin{gathered} D=11\text{m} \\ r=D/2=11/2=\frac{11}{2}=5.5\text{m} \\ {S}_0=4\pi \cdot r^2=4\cdot 3.1416\cdot 5.5^2\doteq 380.1327{\text{m}}^2 \\ S=\frac{1}{2}\cdot 2\cdot S_0=\frac{1}{2}\cdot 2\cdot 380.1327\doteq 380.1327{\text{m}}^2 \\ {S}_1=7.3{\text{m}}^2 \\ b=S/S_1=380.1327/7.3=52.073\text{kg} \end{gathered}$$

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

Try another example