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Math  /  Geometry

QuestionA technical machinist is asked to build a cubical steel tank that will hold 525 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m . □\square m

Studdy Solution

STEP 1

1. The volume of the tank is given in liters (L), and we need to convert it to cubic meters (m³) for consistency in units.
2. The tank is cubical, so its volume can be expressed as V=s3 V = s^3 , where s s is the side length of the cube.
3. The problem requires finding the side length s s in meters and rounding it to the nearest 0.01 m.

STEP 2

1. Convert the volume from liters to cubic meters.
2. Set up the equation for the volume of a cube.
3. Solve for the side length s s .
4. Round the side length to the nearest 0.01 m.

STEP 3

Convert the volume from liters to cubic meters. Since 1 liter is equal to 0.001 cubic meters, we have:
525 L=525×0.001 m3=0.525 m3 525 \text{ L} = 525 \times 0.001 \text{ m}^3 = 0.525 \text{ m}^3

STEP 4

Set up the equation for the volume of a cube, where V=s3 V = s^3 :
s3=0.525 m3 s^3 = 0.525 \text{ m}^3

STEP 5

Solve for the side length s s by taking the cube root of both sides:
s=0.5253 s = \sqrt[3]{0.525}

STEP 6

Calculate the cube root to find s s :
s≈0.5253≈0.809 m s \approx \sqrt[3]{0.525} \approx 0.809 \text{ m}

STEP 7

Round the side length to the nearest 0.01 m:
s≈0.81 m s \approx 0.81 \text{ m}
Solution: The smallest possible inside length of the tank is approximately 0.81 0.81 meters.

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