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A technical machinist is asked to build a cubical steel tank that will hold 415 L of water.Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.001 m.

Answer :

we have

1 cubic meter = 1000 L

x cubic meter = 415 L

then:

[tex]\begin{gathered} 1000\times x=415\times1 \\ 1000x=415 \\ \frac{1000x}{1000}=\frac{415}{1000} \\ x=0.415 \end{gathered}[/tex]

The volume of a cube with length x is:

[tex]\begin{gathered} x^3=0.415 \\ \sqrt[3]{x^3}=\sqrt[3]{0.415} \\ x=0.746 \end{gathered}[/tex]

answer: The smallest possible inside length of the tank is 0.746 m

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