Half-cylinder 9961

The cattle water feeding trough is a half-cylinder with a length of 2 m and a width of 0.8 m. How many m³ of water can be poured into the gutter? How many m² do we need to produce 25 such gutters?

Correct answer:

V₁ =  0.5027 m³
S =  62.8319 m²

Step-by-step explanation:

$$\begin{gathered} l=2\text{m} \\ D=0.8\text{m} \\ r=D/2=0.8/2=\frac{2}{5}=0.4\text{m} \\ {V}_1=\frac{1}{2}\cdot \pi \cdot r^2\cdot l=\frac{1}{2}\cdot 3.1416\cdot 0.4^2\cdot 2=0.5027{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} n=25 \\ {S}_1=\pi \cdot r\cdot l=3.1416\cdot 0.4\cdot 2\doteq 2.5133{\text{m}}^2 \\ S=n\cdot S_1=25\cdot 2.5133=62.8319{\text{m}}^2 \end{gathered}$$

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