Questions: Finding the side length of a cube from its volume in liters A technical machinist is asked to build a cubical steel tank that will hold 190 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m.

Solution Steps

• Given volume of the cube is 190 liters.
• Convert liters to cubic meters using the conversion \(1 \, \text{liter} = 0.001 \, \text{cubic meters}\).
• Therefore, \(190 \, \text{liters} = 190 \times 0.001 \, \text{cubic meters} = 0.19 \, \text{cubic meters}\).

• The formula for the volume of a cube is \(V = s^3\), where \(s\) is the side length.
• Set the volume equal to the converted volume: \(s^3 = 0.19 \, \text{cubic meters}\).

• Solve for \(s\) by taking the cube root of both sides: \(s = \sqrt[3]{0.19}\).
• Calculate \(s\) using a calculator: \(s \approx 0.574 \, \text{meters}\).

• Round the calculated side length to the nearest 0.01 meters.
• \(s \approx 0.57 \, \text{meters}\).

Final Answer