Gutter Sheet Metal Area

Gutters have the shape of half a cylinder. Their diameter is 16 cm, and the total length around the roof is 32.6 m. How many m² of sheet metal are needed to make them? Add 15% for connections and cleaning.

Final Answer:

A =  9.4223 m²

Step-by-step explanation:

$$\begin{gathered} D=16/100=\frac{4}{25}=0.16\text{m} \\ r=D/2=0.16/2=\frac{2}{25}=0.08\text{m} \\ l=32.6\text{m} \\ {S}_1=\pi \cdot D\cdot l=3.1416\cdot 0.16\cdot 32.6\doteq 16.3865{\text{m}}^2 \\ q=1+15/100=\frac{23}{20}=1.15 \\ A=S_1/2\cdot q=16.3865/2\cdot 1.15=9.4223{\text{m}}^2 \end{gathered}$$

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