Sheet metal troughs

A farmer orders sheet metal troughs from a tinsmith for watering calves on pasture. The tinsmith looks at a drawing of the trough and estimates how much sheet metal will be needed for one trough. Determine the sheet metal consumption, adding 15% for waste and seams. The trough has a diameter of 0.5 m and a length of 1.5 m.

Final Answer:

S =  1.5806 m²

Step-by-step explanation:

$$\begin{gathered} q=100\%+15\%=1+\frac{15}{100}=1.15 \\ D=0.5\text{m} \\ L=1.5\text{m} \\ r=D/2=0.5/2=\frac{1}{4}=0.25\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.25^2\doteq 0.1963{\text{m}}^2 \\ o=\pi \cdot D/2=3.1416\cdot 0.5/2\doteq 0.7854\text{m} \\ {S}_2=o\cdot L=0.7854\cdot 1.5\doteq 1.1781{\text{m}}^2 \\ {S}_3=S_1+S_2=0.1963+1.1781\doteq 1.3744{\text{m}}^2 \\ S=q\cdot S_3=1.15\cdot 1.3744=1.5806{\text{m}}^2 \end{gathered}$$

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