Step 1 :A technical machinist is asked to build a cubical steel tank that will hold 75 L of water. We are asked to calculate in meters the smallest possible inside length of the tank. We are to round our answer to the nearest 0.01 m.
Step 2 :The volume of a cube is given by the formula \(V = a^3\) where \(a\) is the length of one side of the cube. We know that the volume of the tank is 75 L, which is equivalent to 0.075 m^3 (since 1 L = 0.001 m^3).
Step 3 :We can solve for \(a\) by taking the cube root of the volume. So, \(a = \sqrt[3]{V}\).
Step 4 :Substituting the given volume into the equation, we get \(a = \sqrt[3]{0.075}\).
Step 5 :Calculating the cube root of 0.075, we get \(a = 0.42\).
Step 6 :Final Answer: The smallest possible inside length of the tank is \(\boxed{0.42 \mathrm{~m}}\).