Calculating the Volume of the Barrel

Oct 13, 2025 by leolavanderia.com.br 23 views

Introduction

A cylindrical rain barrel with a diameter of 2.5 feet and a height of 3.5 feet is filled to a height of 1.5 feet. The problem requires us to determine how many more gallons of water the barrel can hold. To solve this problem, we need to calculate the volume of the barrel and subtract the volume of water already present.

Understanding the Problem

The problem involves a cylindrical rain barrel with specific dimensions. We are given the diameter (2.5 feet) and height (3.5 feet) of the barrel, as well as the height to which it is filled (1.5 feet). We need to calculate the remaining capacity of the barrel, which is the volume of water it can hold beyond the current level.

Calculating the Volume of the Barrel

The formula to calculate the volume of a cylinder is:

V = πr^2h

where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

First, we need to find the radius of the barrel. Since the diameter is given as 2.5 feet, the radius is half of the diameter:

r = 2.5 / 2 = 1.25 feet

Now, we can calculate the volume of the barrel using the formula:

V = π(1.25)^2(3.5) = 3.14(1.5625)(3.5) = 21.69 cubic feet

Converting Cubic Feet to Gallons

Since the problem requires us to find the remaining capacity in gallons, we need to convert the volume from cubic feet to gallons. We are given that 1 foot is equal to 7.5 gallons. Therefore, we can convert the volume as follows:

21.69 cubic feet x (7.5 gallons / 1 foot^3) = 162.52 gallons

Calculating the Remaining Capacity

The barrel is filled to a height of 1.5 feet. To find the volume of water already present, we can use the same formula:

V = πr^2h

Substituting the values, we get:

V = 3.14(1.25)^2(1.5) = 3.14(1.5625)(1.5) = 6.93 cubic feet

Converting this volume to gallons, we get:

6.93 cubic feet x (7.5 gallons / 1 foot^3) = 51.99 gallons

Finding the Remaining Capacity

To find the remaining capacity of the barrel, we subtract the volume of water already present from the total volume of the barrel:

Remaining capacity = Total volume - Volume of water already present = 162.52 gallons - 51.99 gallons = 110.53 gallons

Rounding this value to the nearest whole number, we get:

110 gallons

Q: What is the purpose of a cylindrical rain barrel?

A: A cylindrical rain barrel is a container used to collect and store rainwater from rooftops or other surfaces. The collected rainwater can be used for various purposes, such as watering plants, washing cars, or even providing a source of drinking water in emergency situations.

Q: How do I choose the right size of a cylindrical rain barrel for my needs?

A: To choose the right size of a cylindrical rain barrel, you need to consider the amount of rainfall your area receives, the size of your roof, and the intended use of the collected rainwater. A general rule of thumb is to choose a barrel that can hold at least 50-100 gallons of water.

Q: What are the benefits of using a cylindrical rain barrel?

A: Some of the benefits of using a cylindrical rain barrel include:

Reduced stormwater runoff and erosion
Conserved water for non-potable uses
Reduced water bills
Reduced pressure on municipal water supplies
Aesthetic appeal and educational value

Q: How do I install a cylindrical rain barrel?

A: To install a cylindrical rain barrel, you will need to:

Choose a suitable location for the barrel, such as under a downspout or in a shaded area
Connect the barrel to a downspout or gutter system
Install a first flush device to divert debris and contaminants from the barrel
Connect a spigot or hose to the barrel for easy access to the collected rainwater

Q: How do I maintain a cylindrical rain barrel?

A: To maintain a cylindrical rain barrel, you should:

Regularly inspect the barrel for signs of wear or damage
Clean the barrel and its components regularly
Check the barrel's water level and top it off as needed
Consider adding a mosquito net or other screening to prevent mosquito breeding

Q: Can I use a cylindrical rain barrel for drinking water?

A: While a cylindrical rain barrel can be a useful source of water for non-potable uses, it is not recommended for drinking water. Rainwater can contain contaminants such as bacteria, viruses, and other pollutants that can make you sick. If you plan to use the collected rainwater for drinking, you should consider adding a treatment system, such as a filter or UV purifier.

Q: Are cylindrical rain barrels safe for children and pets?

A: Cylindrical rain barrels can be a hazard for children and pets if not properly secured. Make sure to:

Install the barrel in a safe location, away from walkways and play areas
Use a secure lid or cover to prevent accidental entry
Consider adding a fence or other barrier to prevent access to the barrel

Q: Can I use a cylindrical rain barrel in cold climates?

A: While a cylindrical rain barrel can be used in cold climates, you should consider the following:

Choose a barrel made from durable, frost-resistant materials
Consider adding a heating system or insulation to prevent freezing
Regularly inspect the barrel for signs of damage or wear

Q: How long does a cylindrical rain barrel last?

A: The lifespan of a cylindrical rain barrel depends on various factors, such as the quality of the barrel, maintenance, and usage. On average, a well-maintained cylindrical rain barrel can last for 10-20 years or more.