Cubic feet is the unit of volume that is used to find the volume of three-dimensional solid objects in cubic feet such as rooms, Containers, and cube boxes. The term “cubic” represent the three dimensions (length, width, height), and “feet” is the unit of measurement for the volume of the objects.
Cubic feet are used in various ways such as measuring the capacity of rooms, calculating the volume of objects or containers, estimating the space required for storage of tanks, and determining quantities of materials required like wood, soil, or liquids to fill the container or cube box.
In this article, we discuss the definition of cubic feet, its basic formula, discuss how to evaluate it, and solve the different examples to understand the idea of cubic feet.
Brief idea about Cubic Feet
Cubic feet are a unit of volume that is used to measure the amount of space occupied by an object or the capacity of a container and solid objects in three dimensions. The standard abbreviation for cubic feet is "ft³" or "cu ft”. One cubic feet is equal to the multiple of the length of sides of the cube that are each one foot long.
Multiply the object or container's length, breadth, and height to determine its volume in cubic feet. For example, if you have a rectangular box that measures 2 feet in length, 3 feet in width, and 4 feet in height then the volume is obtained as 2 ft × 3 ft × 4 ft = 24 ft³.
Formulas of Cubic Feet
There are different formulas are given which depend on the shape and size of the objects that are under observation. Here are the formulas for different shapes are given below.Cuboid or Rectangular Prism:
Volume (ft3) = Length (in feet) × Width (in feet) × Height (in feet)V (ft3) =L (in feet) × W (in feet) × H (in feet)
Cube:
Volume (ft3) = Side Length (in feet) × Side Length (in feet) × Side Length (in feet)V (ft3) =L (in feet) × L (in feet) × L (in feet)
Cylinder:
Volume (ft3) = Ï€ × (Radius)2 (in feet)² × Height (in feet)V (ft3) = Ï€ × (R)2 (in feet)² × H (in feet)
Sphere:
Volume (ft3) = (4/3) × Ï€ × (Radius)3 (in feet)³V (ft3) = (4/3) × Ï€ × (R3) (in feet)³
Cone:
Volume (ft3) = (1/3) × Ï€ × (Radius)2 (in feet)² × Height (in feet)
V (ft3) = (1/3) × Ï€ × (R2) (in feet)² × H (in feet)
Note: where the value of (Ï€ is approximately 3.14159 or 22/7) used to find the solution of the above formulas.
How to determine the Cubic Feet from the formula:
- Firstly, identify the shape which is given and used the suitable formula associated with the shape.
- If the length of the given shape is given in feet the used it simply and if it is not given in feet then first convert them into feet to find the solution in feet.
Example 1:
A cubic drawing room with a width of 10 feet, a length of 20 feet, and a height of 5 feet. Find the volume of the drawing room in cubic feet.
Solution:
To find the volume of the drawing room in cubic feet, we use the formula of the cuboid.
Step 1:
Write the data from the given question.
Length = 20 feet, width = 10 feet, Height = 5, v =?
Step 2:
Write the formula of a cuboid to find the volume of the drawing room.
Volume (ft3) = Length (in feet) × Width (in feet) × Height (in feet)
V (ft3) =L (in feet) × W (in feet) × H (in feet)
V = L x W x H
Where V denotes the volume, L is the length, W is the width, and H is the height.
Step 3:
Put the values in the above formula to find the volume and simplify.
L = 20 feet, w = 10, H = 5
V = 20 feet x 10 feet x 5 feet
V = 1000 ft3
You can also take assistance from online tools to calculate cubic feet with steps in few seconds.
Example 2:
Determine the volume of the cone in cubic feet if its height is 36 and the radius is 16.
Solution:
To find the volume of the cone in cubic feet, we use the formula of the cone.
Step 1:
Write the data from the given question.
h = 36, r = 16, V =?.
Step 2:
Write the formula of the volume of a cone.
Volume (ft3) = (1/3) × Ï€ × (Radius)2 (in feet)² × Height (in feet)
V (ft3) = (1/3) × Ï€ × (R2) (in feet)² × H (in feet)
V = (1/3)[Ï€r²h]
Step 3:
Put the values in the above formula to find the volume and simplify.
h = 36, r = 16
V = (1/3)[Ï€r²h]
V = (1/3)[Ï€(16)2(36)]
V = (1/3)[28964.57]
V = 964.86 ft3
Example 3:
If the rectangular box length is 10 feet, width is 6 feet, and height is equal to 7 feet then determine the volume in cubic feet.
Solution:
To find the volume of the rectangular box in cubic feet, we use the formula of the cuboid.
Step 1:
Writethe data carefully from the above question.
Length = 10, Width = 6, Height = 7, Volume =?
Step 2:
Write the formula of a rectangular prism to find the volume in cubic feet.
Volume (ft3) = Length (in feet) × Width (in feet) × Height (in feet)
V (ft3) =L (in feet) × W (in feet) × H (in feet)
V = L x W x H
Where V denotes the volume, L is the length, W is the width, and H is the height.
Step 3:
Put the values in the above formula to find the volume and simplify.
L = 10, W = 6, H = 7
V = L x W x H
V = 10 x 6 x 7
V = 420 ft3
Final Words
In this article, we discussed the basic definition of cubic feet, its different formulas, and methods to evaluate them. Moreover, to better understand the concept of cubic feet solved different examples in detail using different shapes.
By reading of this article, anyone can solve the related problem easily.
