Sheet metal troughs

A farmer orders sheet metal troughs from a tinsmith for loading calves on pasture. The tinsmith looks at a picture of the trough and estimates how much sheet metal he will need for one trough. Determine the sheet metal consumption, add 15% for waste and joints. The diameter is 0.5m and the length is 1.5m

Correct 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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