Sand sieve coarse

At the construction site, the sand that belongs to the mortar is sifted through a sieve. At the same time, 1/6 of the coarse sand falls through. Determine how many m³ of sand must be brought in to obtain 2 m³ of sifted sand.

Final Answer:

V₁ =  2.4 m³

Step-by-step explanation:

$$\begin{gathered} V_2=2{\text{m}}^3 \\ r=1-\frac{1}{6}=\frac{1\cdot 6}{6}-\frac{1}{6}=\frac{6}{6}-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}\doteq 0.8333 \\ {V}_1\cdot r=V_2 \\ {V}_1=V_2/r=2/\frac{5}{6}=2:\frac{5}{6}=2\cdot \frac{6}{5}=\frac{2\cdot 6}{5}=\frac{12}{5}=\frac{12}{5}{\text{m}}^3=2.4{\text{m}}^3 \end{gathered}$$

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