A technical machinist is asked to build a cubical steel tank that will hold 65L of water. Calculate, in meters, the smallest possible inside length of the tank. Round your answer to the nearest 0.001m.
The correct answer and explanation is:
To find the smallest possible inside length of the cubical steel tank, we need to calculate the side length of a cube that can hold 65 liters of water. The volume of a cube is given by the formula: V=s3V = s^3
Where VV is the volume of the cube and ss is the side length of the cube. Since 1 liter equals 1 cubic decimeter (dm³), 65 liters is equal to 65,000 cubic centimeters (cm³). Since 1 cubic meter equals 1,000,000 cubic centimeters (cm³), we can convert the volume to cubic meters: V=65L=65 dm3=0.065 m3V = 65L = 65 \, \text{dm}^3 = 0.065 \, \text{m}^3
Now, we solve for ss by taking the cube root of the volume: s=0.0653s = \sqrt[3]{0.065} s≈0.408s \approx 0.408
Thus, the smallest possible inside length of the cubical tank is approximately 0.408 meters when rounded to the nearest 0.001 meter.
This solution is based on the geometry of a cube. A cube has equal side lengths, and the volume is calculated by cubing the side length. Since the volume of water that the tank must hold is given as 65 liters, we first convert that volume to cubic meters to make the calculation easier. After solving the cube root of the volume, we find that the side length of the cube that will hold this volume is 0.408 meters.
This calculation assumes the tank has perfect cubical dimensions, and it gives the smallest possible inside length, meaning the tank’s side length is the shortest distance needed to contain 65 liters of water.