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 0.001 m.

Solution Steps

To find the side length of a cube given its volume, we need to take the cube root of the volume. Since the volume is given in liters, and 1 liter is equivalent to 0.001 cubic meters, we first convert the volume from liters to cubic meters. Then, we calculate the cube root of the volume in cubic meters to find the side length of the cube. Finally, we round the result to the nearest 0.001 meters.

The volume of the tank is given as \( V = 190 \) liters. To convert this to cubic meters, we use the conversion factor \( 1 \, \text{L} = 0.001 \, \text{m}^3 \): \[ V = 190 \, \text{L} \times 0.001 \, \text{m}^3/\text{L} = 0.19 \, \text{m}^3 \]

The volume of a cube is given by the formula \( V = s^3 \), where \( s \) is the side length. To find \( s \), we take the cube root of the volume: \[ s = \sqrt[3]{V} = \sqrt[3]{0.19} \approx 0.5749 \, \text{m} \]

We round the calculated side length to the nearest \( 0.001 \) meters: \[ s \approx 0.575 \, \text{m} \]

Final Answer