Questions: Knowledge Check Question 12 Camron Joel A technical machinist is asked to build a cubical steel tank that will hold 360 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m . m

Knowledge Check Question 12 Camron Joel A technical machinist is asked to build a cubical steel tank that will hold 360 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m . m
Transcript text: Knowledge Check Question 12 Camron Joel A technical machinist is asked to build a cubical steel tank that will hold 360 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m . $\square$ $\square \mathrm{m}$ I Don't Know Submit Terms of Use Privacy Center Accessibility
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Solution

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Solution Steps

To find the smallest possible inside length of a cubical tank that can hold 360 liters of water, we need to determine the side length of a cube whose volume is 360 liters. Since 1 liter is equivalent to 0.001 cubic meters, we first convert the volume to cubic meters. Then, we find the cube root of this volume to get the side length of the cube. Finally, we round the result to the nearest 0.01 meters.

Step 1: Convert Volume to Cubic Meters

The volume of the tank is given as \( 360 \) liters. To convert this to cubic meters, we use the conversion factor \( 1 \, \text{L} = 0.001 \, \text{m}^3 \): \[ \text{Volume in cubic meters} = 360 \, \text{L} \times 0.001 \, \text{m}^3/\text{L} = 0.36 \, \text{m}^3 \]

Step 2: Calculate the Side Length of the Cube

The volume \( V \) of a cube with side length \( s \) is given by the formula: \[ V = s^3 \] To find the side length, we take the cube root of the volume: \[ s = V^{1/3} = (0.36)^{1/3} \approx 0.7114 \, \text{m} \]

Step 3: Round the Side Length

We round the calculated side length to the nearest \( 0.01 \) meters: \[ s \approx 0.71 \, \text{m} \]

Final Answer

The smallest possible inside length of the tank is \\(\boxed{0.71 \, \text{m}}\\).

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