Drinking trough

A drinking trough for cattle is in the shape of a cylinder measuring 2 metres in length and 80 cm in width. How much sheet metal is needed to make it, given that an additional 12% of material is added for joints?

Final Answer:

S =  3.3778 m²

Step-by-step explanation:

$$\begin{gathered} a=2\text{m} \\ D=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m} \\ q=100\%+12\%=1+\frac{12}{100}=1.12 \\ r=D/2=0.8/2=\frac{2}{5}=0.4\text{m} \\ {S}_1=\pi \cdot r\cdot a=3.1416\cdot 0.4\cdot 2\doteq 2.5133{\text{m}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 0.4^2\doteq 0.5027{\text{m}}^2 \\ S=q\cdot (S_1+S_2)=1.12\cdot (2.5133+0.5027)=3.3778{\text{m}}^2 \end{gathered}$$

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