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VOOZH | about |
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VOOZH | about |
Volume of a Cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object. An object with a larger volume would occupy more space. The volume of the cube is calculated by multiplying the length, breadth, and height of the cube. For a cube the length, breadth, and height are equal. Thus, the volume of a cube is just a side cube.
In this article, we will understand the volume of a cube in detail along with the formula and solved examples in the following sections. Also, learn about the Surface area of the cube here.
Table of Content
The volume of a cube is defined as the total capacity of the cube it is the total amount of liquid a cube can hold. The volume of a cube is measured in cubic units such as cm3, m3, etc. A cube is a solid 3-D figure, with 6 square faces. All the faces of a cube are square hence it has all dimensions equal
Let the length, width, and height of a cube be ‘a’, then;
Volume of cube = a × a × a
Volume of Cube = a3
All corners of a cube meet at an angle of 90° degrees. The figure below shows a cube, where l is the length, b is the width, h is the height and l = b = h. The length, width, and height represent the edges of the cube and when three edges meet at a point, it is called a vertex.
👁 Cube StructureVolume of a cube is defined as the total number of cube units that the cube occupies completely. A cube is a three-dimensional shape with six faces, twelve edges, and eight vertices. Therefore, the volume of a cube is the space surrounded by its six faces. Volume of the cube is calculated using two formulas which are discussed below:
Formula to calculate the volume of a cube when the side (Let a) of the cube is given
Volume of Cube = a × a × a = a3
Thus, when the edge length is known volume of the cube can easily be found
Example:Find the volume of a cube with a side of 5 cm
Solution:
Given,
Edge length( a) = 5 cm
Volume = 53
Volume = 5 × 5 × 5 = 125 cm3
Formula to calculate volume of a cube when diagonal of cube is given
Volume of Cube = [√3 × (d)3] / 9
where,
Equation which gives the volume of a cube is discussed below. Suppose a cube of edge length 'a' is taken then its volume is calculated using the formula.
Volume of Cube(V) = a × a × a = a3
For example, what is volume of cube if side length is 7 m?
Solution:
Side of cube =7 m
Volume of cube equation,
v = a3
Putting value of a in above equation we get,
v = (7)3
v = 343 m3
Thus, volume of cone is 343 m3
Volume of any object is the space occupied by that solid in the 3-D plane. In a cube all the sides i.e. length, breadth, and height are equal (l = b = h). Formula for volume of a cube is derived as follows:
Now volume of any regular figure is base area multiplied by height. Thus,
Volume of Cube = Base Area × Height = a2 × a = a3 units3
Two methods by which the volume of a cube can be found are
Volume of a Cube is calculated using the steps discussed below:
Step 1: Note dimension of cube. Let side is represented by (a) and diagonal is represented as (d).
Step 2: Now use formula,
V = a3
OR
V =[√3 × (d)3] / 9
Step 3: Simplify above equation.
Step 4: Add unit3 to answer in step 3 to volume of cube.
As volume of a cube is a cubic function it increases drastically if we change the dimension of the cube. This can be understood by the following image.
👁 Increasing Volume of CubeSurface Area of Cube is the total area covered by all the faces of the cube. As a cube has six square faces of similar dimensions its volume is calculated by the formula,
Surface Area of Cube = 6a2
where,
Cube is a three-dimensional figure with six faces and three dimensions length, breadth, and height but for a cube all the dimension length = breadth = height = a(say). Then its volume is given as,
Volume = a3
Cuboid is a three-dimensional figure with six faces and three dimensions length, breadth, and Height (l, b, and h) respectively then volume of cuboid is given by the formula:
Volume = l × b × h
Various examples which we come across in our daily life resembles cube and we are required to find their volume. Some of the common examples are,
Example 1: If the volume of a cube is 216 cm3, what is the dimension of the cube?
Solution:
Given,
Volume of a cube, V = 216 cm3
Volume of cube = (side)3
V = (216) = (6)3
Therefore, side of cube is 6 cm
Example 2: How many 3 cm × 3 cm × 3 cm cube boxes can fit in a large 15 cm cube box?
Solution:
Volume of each box = (3 × 3 × 3) cm3 = 27 cm3
Volume of large cube box = (15 × 15 × 15) cm3 = 3375 cm3
Number of boxes(N) = (Volume of Large Cube) / (Volume of Small Cube)
N = 3375cm3 / 27cm3
N =125 boxes
Thus, 125 boxes are required to fit in the large box.
Example 3: Volume of a cubic hard disk is 0.5 dm3. What are dimensions of disk?
Solution:
Volume of a Cube = a3
0.5 = a3
a = 3√0.5
a = 0.794 dm
Example 4: Calculate volume of a cube with a diagonal of 3 inches.
Solution:
Given,
Diagonal = 9 inch
Cube Volume = [√3 × (Diagonal)3] / 9
Volume(V) = √3×[(3)3/9]
V = √3 × 3
V = 1.732 × 3
V = 5.196 inches3
Example 5: Find edge of a cube whose volume is 1000 cm3
Solution:
Volume = 1000 cm3
Volume = a3
1000 = 103 = a3
a (edge) = 10 cm
Thus, edge of cube is 10 cm.
Example 6: Find volume of a cube of side 0.01 cm
Solution:
Given,
Edge (a) = 0.01 cm
Volume = a3
Volume(V) = (0.01)3
V = 0.000001 cm3
Thus, volume of cube is 10-6 cm3
Problem 1: A cube has a side length of 6 cm. Find its volume.
Problem 2: If the volume of a cube is 125 cubic units, what is the length of one side?
Problem 3: The volume of a cube is 512 cubic centimeters. Find the length of one side.
Problem 4: If the volume of a cube is 343 cubic meters, what is the length of one side?
Problem 5: A cube has a volume of 1000 cubic inches. Find the length of one side.
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