7.48 Gallons: The Quandary of Volume in a Linear Measurement

Understanding the Conceptual Divide

When we measure the volume of a substance, we typically think in terms of cubic units, such as gallons or cubic feet. However, when we measure the length of an object, we use linear units, such as feet or inches. This can lead to confusion when trying to relate the volume of a substance to its linear dimensions.

The Case of Gallons in a Foot

One common example of this confusion is the question of how many gallons of water are contained in a foot of pipe. To answer this question, we need to understand the relationship between the volume of a cylinder and its radius and height.

The volume of a cylinder is given by the formula:

V = πr²h

where:

• V is the volume of the cylinder in cubic units
• π is a mathematical constant approximately equal to 3.14
• r is the radius of the cylinder in linear units
• h is the height of the cylinder in linear units

Applying the Formula to a Pipe

If we assume that the pipe is a perfect cylinder, then we can use the formula above to calculate the volume of water that it can hold. Let's say that the pipe has a diameter of 1 foot, which means that its radius is 0.5 feet. If we also assume that the pipe is 1 foot long, then we can calculate the volume of water that it can hold as follows:

V = π(0.5 ft)²(1 ft) = 0.785 ft³

However, 1 cubic foot is equal to 7.48 gallons, so the pipe can hold approximately 7.48 gallons of water.

Practical Applications

Understanding the relationship between gallons and feet can be useful in a variety of practical applications, such as:

• Estimating the volume of a water tank: If you know the diameter and height of a water tank, you can use the formula above to calculate its volume in cubic feet. You can then convert this volume to gallons by multiplying by 7.48.
• Sizing a water pump: If you need to pump water from a well or other source, you need to know how many gallons per minute the pump can handle. To determine this, you need to know the flow rate of the pump in cubic feet per minute and then convert this to gallons per minute by multiplying by 7.48.
• Calculating the cost of water: If you are billed for water based on the number of gallons you use, you need to know how to convert cubic feet to gallons. To do this, simply multiply the number of cubic feet by 7.48.

Conclusion

Understanding the relationship between gallons and feet is important for a variety of practical applications. By using the formula V = πr²h, you can calculate the volume of any cylinder, including a pipe. This information can be used to estimate the volume of a water tank, size a water pump, or calculate the cost of water.