What are Cubic Feet? Its Formula, Application, and Explanation

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In mathematics, cubic feet are a unit of measurement used to measure volume in three-dimensional space. It is generally used to measure the capacity or volume of objects such as rooms, buildings, containers, and natural resources like water or air.

The modern standardization of this unit took place in the 18th century, particularly in English-speaking countries. It became widely adopted as a unit of volume measurement particularly in the United States While cubic feet are widely used in countries that have adopted the metric system, cubic meters (m³) are the preferred unit of volume measurement.

What are Cubic Feet? Its Formula, Application, and Explanation

Today, it is used in various industries, including construction, architecture, engineering, and manufacturing. It provides a standardized unit of measurement for volume allowing for easy communication and comparison of volumes across different applications.

In this article, we will discuss the basic definition of this, units in detail, and their applications.

What are cubic feet?

The quantity of volume engaged by an item or section in three dimensions is measured in cubic feet. It is generally used in the Imperial arrangement and United States customary units.

The representation for this unit is “ft³” or “cu ft.” It is essential to communicate that the actual numerical value of a volume measured in cubic feet can vary widely depending on the specific dimensions of the object or space being measured.

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Cubic feet formula:

The formula to calculate the volume in cubic feet depends on the shape of the object being measured. Here are the formulas for calculating the volume in cubic feet for some common shapes:

Cube:

If all sides of the cube measure “a” foot, then the volume in cubic feet is given by:

a³ = a x a x a = Volume

Rectangular Prism:

In mathematically representing the length, width, and height of the rectangular prism are “l,” “w,” and “h” feet correspondingly, then the volume in cubic feet is given by:

Volume = l × w × h

  • l = length
  • w = width
  • h = height

Units of volume

Here are some different units of volume that can be used as alternatives to cubic feet:

Unitsdetails
Cubic Inches (in³):One cubic foot is equivalent to 1,728 cubic inches.
Cubic Yards (yd³)One cubic yard is equal to 27 cubic feet
Cubic Meters (m³):One cubic meter is approximately 35.3147 cubic feet
Liters (L):One liter is approximately 0.0353 cubic feet
Barrels (bbl):  One cubic barrel is approximately 5.6146 cubic feet or 42 gallons.  

Example:  Calculate the volume of a box having dimensions 4 m × 5 m × 7 m in cubic feet.

Solution: The volume of the box = 4 m × 5 m × 7 m = 140 m3

 As one cubic meter is approximately equal to 35.3147 cubic feet.

Thus, 140 m3 = 140 × 35.3147 = 4,944.058 ft3.

Hence, the volume of a box in cubic feet is approximately 4,944.058 ft3

Applications of cubic feet

Cubic feet have various applications across different industries and everyday life. Here are some common applications of cubic feet:

  • Construction and Architecture
  • Shipping and Logistics
  • Air Conditioning and HVAC
  • Moving and Removals
  • Petroleum and Natural Gas
  • Geological and Environmental Studies

1.     Construction and Architecture:

Cubic feet are used to measure the volume of building materials such as concrete, lumber, or gravel, needed for construction projects. It helps in estimating quantities accurately and planning for material procurement.

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2.     Shipping and Logistics:

It is used to measure the capacity of shipping containers, cargo holds, and storage spaces. It helps in optimizing load planning maximizing space utilization and calculating shipping costs.

3.     Air Conditioning and HVAC:

It is used to assess the cooling or heating capacity required for a space. It helps determine the appropriate size of air conditioning units and HVAC systems to efficiently regulate temperature.

4.     Moving and Removals:

It is used to estimate the volume of belongings when planning a move or removal. It helps determine the size of moving trucks or storage units needed and assists in cost estimation.

5.     Petroleum and Natural Gas:

It is used to quantify the volume of natural gas or petroleum reserves. It plays a crucial role in resource estimation, pricing, and energy production planning.

6.     Geological and Environmental Studies:

It is used to measure the volume of geological formations, water bodies, and air pollutants. It assists in environmental assessments resource management and pollution control.

Examples of Finding Volume

In this section, we are going to discuss finding volume in cubic feet with the help of examples. Calculating it is not a difficult task; you have to take the measurements of a cuboid and make all those measurements in the same unit, and multiply them.

Example 1:

What is the volume of a rectangular box with dimensions 4 feet length, 3 feet width, and 2 feet height?

Solution:

Step 1:

Identify the dimensions of a rectangular box are:

L = Length = 4 feet

W = Width = 3 feet

H = Height = 2 feet

Step 2:

Mathematically form of cubic feet is

V = Volume = L x W x H = Length × Width × Height

Step 3:

We put the values in a given formula.

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Volume = 4 feet × 3 feet × 2 feet

Step 4:

Multiply the numbers together:

Volume = 24 cu. ft

Step 5:

Therefore, the volume of the rectangular box with dimensions 4 feet in length, 3 feet in width, and 2 feet in height are 24 cubic feet.

Example 2:

How many cubic feet of soil is needed to fill a rectangular planter with dimensions 5 feet length, 3 feet width, and 2 feet height?

Solution:

The given dimensions of the planter are:

Length = 5 feet

Width = 3 feet

Height = 2 feet

Step 2:

Now we write the cubic rectangular shape formula as:

V = Volume = L x W x H = Length × Width × Height

Step 3:

We put the value of the given formula is

Volume = 5 feet × 3 feet × 2 feet

Step 4:

Multiply the numbers together is

Volume = 30 cu. ft

Step 5:

Therefore, the volume of soil needed to fill the rectangular planter with dimensions 5 feet in length, 3 feet in width, and 2 feet in height is 30 cubic feet.

Summary

In this article, we have discussed the basic definition of cubic feet, units, and their applications. Moreover, with the help of examples defined this topic in detail. Now you can completely understand this article, anyone can easily solve any problem related to cubic feet.

I hope this article will help you to understand What are Cubic Feet? Its Formula, Application, and Explanation. You may also want to see my other post on my Blog. If I have missed anything here, please let me know about that in the comment below this post.

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About Author

Umair Nawaz

Umair Nawaz, a Civil Engineer and passionate part-time blogger, shares his 4 years of knowledge and experiences through engaging articles on civil engineering sites. Join him on a journey of discovery as he makes the world of civil engineering accessible and exciting for all.

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