4 Ways to Calculate the Volume of a Cube
Volume of the cube is s3 as all sides of the cube are equal. In this article, we will learn four methods of calculating the volume of cube: using side, diagonal, area and volume of smaller cubes.
We will also discuss the basics of the cubes and the formula for the volume of a cube and solve some examples related to the volume of a cube.
What is Volume of Cube?
The region bounded by the cube in the three-dimensional space is called the volume of a cube. It is measured in cubic units. A cube is a three-dimensional figure with all its sides equal so, the volume of the cube is given by length × breadth × height i.e., side × side × side cubic units.
4 Ways to Calculate Volume of Cube
The four ways to calculate the volume of the cube are:
- Volume by Side of Cube
- Volume by Diagonal of Cube
- Volume by Area of Cube
- Volume by Volume of Smaller Cube
Volume by Side of Cube
The volume by side of the cube is given by:
Volume of cube = s3
where,
- s is side of cube
Example: Find the volume of cube with side length 20 units.
Solution:
To find the volume of cube we use formula
Volume of cube = s3
Volume of cube = 203
Volume of cube = 8000 cubic units.
The volume of given cube is 8000 cubic units.
Volume by Diagonal of Cube
The volume of cube formula by diagonal of cube is given by:
Volume of cube = (D / √3)3
where,
- D is the diagonal of cube.
Example: Find the volume of the cube with diagonal 30 units.
Solution:
To find the volume of cube we use formula
Volume of cube = (D / √3)3
Volume of cube = (30 / √3)3
Volume of cube = (10√3)3
Volume of cube = 3000√3 = 5196.15 cubic units
The volume of given cube is 5196.15 cubic units.
Volume by Area of Cube
The volume of cube formula by area of cube is given by:
Volume of cube = [√(A/6)]3
where,
- A is the area of cube
Example: Calculate the volume of cube given the area of cube is 96 square units.
Solution:
To find the volume of cube we use formula
Volume of cube = [√(A/6)]3
Volume of cube = [√(96/6)]3
Volume of cube = [√16]3
Volume of cube = 43
Volume of cube = 64 cubic units
The volume of given cube is 64 cubic units.
Volume by Volume of Smaller Cube
The volume of cube using the volume of smaller cube is given by:
Volume of bigger cube = N × Vs
where,
- N is number of smaller cube
- Vs is volume of smaller cube
Example: Calculate the volume of cube if the cube is divided into 27 smaller cubes with volume 150 cubic units.
Solution:
To find the volume of cube we use formula
Volume of bigger cube = N × Vs
Volume of bigger cube = 27 × 150
Volume of bigger cube = 4050 cubic units
The volume of given cube is 4050 cubic units.
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Solved Examples on Volume of Cube
Example 1: Find the volume of cube with side length 11 units.
Solution:
To find the volume of cube we use formula
Volume of cube = s3
Volume of cube = 113
Volume of cube = 1331 cubic units.
The volume of given cube is 1331 cubic units.
Example 2: Find the volume of the cube with diagonal 15 units.
Solution:
To find the volume of cube we use formula
Volume of cube = (D / √3)3
Volume of cube = (15 / √3)3
Volume of cube = (5√3)3
Volume of cube = 649.5 cubic units
The volume of given cube is 649.5 cubic units.
Example 3: Calculate the volume of cube given the area of cube is 24 square units.
Solution:
To find the volume of cube we use formula
Volume of cube = [√(A/6)]3
Volume of cube = [√(24/6)]3
Volume of cube = [√4]3
Volume of cube = 23
Volume of cube = 8 cubic units
The volume of given cube is 8 cubic units.
Example 4: Calculate the volume of cube if the cube is divided into 4 smaller cubes with volume 200 cubic units.
Solution:
To find the volume of cube we use formula
Volume of bigger cube = N × Vs
Volume of bigger cube = 4 × 200
Volume of bigger cube = 800 cubic units
The volume of given cube is 800 cubic units.
Practice Questions on Volume of Cube
Q1. Find the volume of cube with side length 6 units.
Q2. Determine the volume of cube if the diagonal of cube is 18 units.
Q3. Calculate the volume of cube given that the area of the cube is 54 sq. units.
Q4. Calculate the volume of bigger cube if the cube is divided into 64 smaller cubes with volume 30 cubic units.
Q5. Find the side of the cube given the volume of cube is 343 cubic units.
FAQs on Volume of Cube
What is Volume of Cube?
The volume of cube is the region bounded by the cube in 3-D space.
What is the Formula for Volume of Cube?
The formula for volume of a cube is given by:
Volume of cube = (s)3
where, s is side of cube.
How Can You Calculate the Volume of a Cube?
To calculate the volume of a cube we first determine the dimensions given in the question. Then, according to the dimensions we apply volume of cube formula.
What is the SI Unit of Volume?
The SI unit of volume is cubic meter.
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