# The observatory

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

Result

S =  210.7 m2

#### Solution:

$r=5.4 \ \text{m} \ \\ \ \\ S_{1}=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 5.4^2 \doteq 366.4354 \ \text{m}^2 \ \\ \ \\ k=1 + 15/100=\dfrac{ 23 }{ 20 }=1.15 \ \\ \ \\ S=S_{1} / 2 \cdot \ k=366.4354 / 2 \cdot \ 1.15 \doteq 210.7003 \doteq 210.7 \ \text{m}^2$

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