Calculating the Volume of a Rectangular Tank with Mixed Units

The question about the volume of a rectangular tank given in mixed units highlights the importance of consistent measurement units in calculations. Let’s break down the steps to determine the tank's volume and ensure all measurements are in the same system before proceeding.

Addressing Mixed Units

The original dimensions of the tank provided are:

Length: 12 feet Width: 3 feet 5 cm (or 3.4166 feet) Height: 1 foot

For consistency in measurements, we should convert all units to either imperial units or metric units. Here, we will use the imperial unit system for calculations.

Converting the Width to Feet

The width is given as 3 feet 5 cm. To convert 5 cm to feet, we use the conversion factor:

5 cm 0.5 inches (since 1 inch 2.54 cm) 0.5 inches ÷ 12 inches/foot 0.04167 feet

Thus, the total width in feet is:

3 feet 0.04167 feet 3.04167 feet

Calculating the Volume

The volume ( V ) of a rectangular tank is given by the formula:

V length times; width times; height

Substituting the values:

V 12 ft times; 3.04167 ft times; 1 ft V ≈ 36.4999 ft3

The volume of water in the tank is approximately 36.5 cubic feet. To convert this volume to gallons, we use the conversion factor:

1 cubic foot ≈ 7.48052 gallons

Thus:

36.5 ft3 times; 7.48052 gallons/ft3 ≈ 273.0283 gallons

Therefore, the tank can hold approximately 273 gallons of water.

Converting to Metric Units

Alternatively, we can convert all dimensions to metric units for a different perspective:

12 feet 3.6576 meters 3.4166 feet 1.041636 meters 1 foot 0.3048 meters

Converting the volume to liters (1 cubic meter 1000 liters):

V 3.6576 m times; 1.041636 m times; 0.3048 m V ≈ 1.21164 m3 1.21164 m3 times; 1000 L/m3 ≈ 1211.64 L

Therefore, the tank can hold approximately 1211.64 liters of water.

Conclusion

Consistency in measurements is crucial for accurate calculations. Whether you choose to work in imperial units (feet and gallons) or metric units (meters and liters), the volume of water in the tank can be calculated as either 273 gallons or 1211.64 liters.

Related Keywords

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