The observatory

The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal need to be covered to cover it, and must we add 15 percent to the minimum amount due to joints and waste?

Correct answer:

S =  210.7003 m²

Step-by-step explanation:

$$\begin{gathered} h=5.4\text{m} \\ r=h=5.4=\frac{27}{5}=5.4\text{m} \\ {S}_1=4\pi \cdot r^2=4\cdot 3.1416\cdot 5.4^2\doteq 366.4354{\text{m}}^2 \\ k=100\%+15\%=1+\frac{15}{100}=1.15 \\ S=S_1/2\cdot k=366.4354/2\cdot 1.15=210.7003{\text{m}}^2 \end{gathered}$$

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