Mastering Cubic Feet: A Comprehensive Guide for Learners

In the study of mathematics, a cubic foot is a three-dimensional measurement unit. It is used to measure the volume covered by an object in the ground or in space. Cubic feet are widely used to measure the sizes, capacities, and volumes of the various objects or regions in different industries, and our daily life uses things, including refrigerators, machines, tables, etc.

The study of mastering cubic feet is essential for construction and architecture, shipping and transportation, and HVAC systems. In this article, we are going to discuss finding volume in cubic feet along with definitions, formulas, conversions, and examples.

Define Cubic Feet

A cubic foot is a unit of measurement used to measure the volume of a cube-shaped object. Specifically, it is the volume of a cube that measures 1 foot on each side.

In other words, a cubic foot is equal to the amount of space that measures 1 foot in length, width, and height. A cubic foot is commonly denoted as “ft³ or cu ft”. It is a unit of volume that measures the amount of space occupied by an object or substance in three dimensions of space.

It is equal to a cube with sides that are each one-foot long. To put it another way, a cubic foot of space is roughly the size of a basketball. This unit of measurement is commonly used in the United States to express quantities of products such as soil, sand, gravel, or construction materials.

Cubic Feet Formulas

Calculating cubic feet involves different formulas that are specific to the shape of the object being measured. Below are several commonly used formulas for calculating cubic feet:

Cubic Feet of a Cube:

The volume of Cube = Length ft x Width ft x Height ft

For example: If a packaging box is 2.2 feet in height, 2.2 feet in width, and 2.2 from front side. Its volume will be equal to (2.2 feet x 2.2 feet x 2.2 feet) = 10.648 ft³

Cubic Feet of a Rectangular Prism:

The volume of Rectangular Prism = (Length x Width x Height) ft³

For example: If a box is 2 feet in height, 1.5 feet in width, and 1 from the front side. Its volume will be equal to (2 feet x 1.5 feet x 1 feet) = 3 ft³

Cubic Feet of a Sphere:

The volume of Sphere = (4/3) x π x (radius ft) ³

For Example: If a basketball has a radius of 0.5 feet, the calculation would be

Volume = (4/3) x π x (0.5)³ = 0.5235 ft³

Cubic Feet of a Cylinder:

The volume of Cylinder = π x (radius ft)² x height ft

Example: If the radius of a cylinder is 1 foot and its height is 10 feet, its volume will be:

Volume = π x (1)² feet x 10 feet = 31.41 ft³

Cubic Feet Conversion into Other Volume Measurements

In the measurement of some cubic objects, we face these scenarios: we get measurements in meters or feet plus inches. To calculate their cubic feet, we convert meters, yards, or inches into feet and then simplify them together. Here are some common factors to convert into feet.

Other Measurement Measurement in feet

1 Cubic Meter 1 x 35.3147 ft³
1 Cubic Inch 1 x 0.0005787 ft³
1 Cubic Liter 1 x 0.0353 ft³
1 Cubic Yard 1 x 27 ft³
1 Cubic Centimeter 1 x 0.000035 ft³

How Cubic Feet Is Calculated?

You can calculate volume in cubic feet manually or using online calculators.

To calculate cubic feet manually:

get the measurements of all dimensions of the object in feet
Put down the all-side measurements of the object in the mentioned formula.
Simplify.

Finding Cubic Feet Using Online Calculator:

Various online platforms provide cubic feet calculators which simplify quick volume calculations. These digital tools are generally free and offer a volume converter function to convert cubic feet to different units of measurement.

To find the volume of an object in cubic feet using an online calculator, we are typically required to input the dimensions (length, width, and height) of the object in feet into the calculator.

Simply enter the measured values of the object and press the “Calculate” button, the calculator will calculate the cubic feet with stepwise calculating. Below are a few online tools that provides a step by step solution of finding volume in cubic feet.

Solved Examples

Example 1:

Find the volume of the cube in feet and yards. If the dimensions are:

Length = 2 meters, Height = 18 inches, Width = 12 feet

Solution:

Given Data:

length = 2 m, width = 12 ft, height = 18 in

Cubic Feet Formula = [Length feet × Width feet × Height feet]

Solution 1 (in Feet):

First of all, converting all units to feet (ft):

Lenth 2 m x 3.28 = 6.562 ft

Height 18 in ÷ 12 = 1.5 ft

The values after conversion are as:

length = 6.562 ft

width = 12 ft

height = 1.5 ft

Putting values in the formula:

Cubic Feet = (6.562 ft × 12 ft × 1.5 ft)

Cubic Feet = 118.116 ft³

Solution 2 (in Yard):

Convert feet into the yard.

1 cubic yard = 27 cubic ft

(118.116 ÷ 27) ft³ = 4.374 cubic yd

Example 2:

Calculate the volume of the cylindrical container. If its radius is 3.5 feet and height is 15 feet.

Solution:

Given Data:

Radius r = 3.5 feet and Heigh h = 15 feet

Volume = πr²h

= π × 3.52 × 15

= 183.75 π

= 577.267 ft³

Wrap Up

This article provides a comprehensive guide for learners on how to master cubic feet. The guide explains formulas for various shapes helping with accurate calculations. It also highlights the importance of change in other volume measurements.

Using an online calculator simplifies the process while ensuring accuracy. Examples make concepts clearer and enhance understanding.