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Volume of Cube
The volume of a cube is defined as the total number of cubic units occupied by the cube completely. To calculate the volume of a cube, we need to know the length of any one side of the cube. The formula for finding the volume of cube is: Volume = side x side x side.
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. Let us understand the volume of a cube in detail along with the formula and solved examples in the following sections.
|1.||What is Volume of Cube?|
|2.||Volume of Cube Formula|
|3.||How To Find the Volume of a Cube?|
|4.||FAQs on Volume of Cube|
What is Volume of Cube?
The volume of a cube is the total three-dimensional space occupied by a cube. A cube is a 3-D solid object with six square faces, having all the sides of the same length. The cube is also known as a regular hexahedron and is one of the five platonic solid shapes.
The unit of volume of the cube is given as the (unit)3 or cubic units. The SI unit of volume is the cubic meter (m3), which is the volume occupied by a cube with each side measuring 1m. The USCS units for volume are inches3, yards3, etc.
Volume of Cube Formula
We can calculate the volume of any cube using different formulas based on the given parameters. It can be calculated using the side length or the measure of the cube's diagonal.
- Volume of a cube (V) whose side is s is, V = s3.
- Volume of the cube (V) whose diagonal is d is, V = (√3×d3)/9
Volume of Cube Using Side Formula
The volume of a cube can be found by multiplying the edge length three times by itself. i.e., the volume of a "cube" is obtained by "cubing" the side length. For instance, if the length of an edge of a cube is 4, the volume will be 43. The formula to calculate the volume of a cube is given as,
Volume of a cube = s3, where 's' is the length of the side of the cube.
The concept to obtain the volume of a cube formula can be understood using the following steps,
- Consider any square-shaped sheet of paper.
- Now, the area covered by this square sheet will be its surface area i.e. its length multiplied by its breadth. As for a square, since the length and breadth are equal, the surface area will be “s2“.
- A cube is made by stacking multiple square sheets on top of each other so that the height becomes equal to the length and breadth, i.e., “s” units.
- This gives us the height or thickness of the cube as “s”.
- It can thus be concluded that the overall space covered by the cube, which is the volume, will be the area of the base multiplied by the height. i.e., s2 × s = s3.
Volume of Cube Using Diagonal Formula
The volume of the cube can also be found out directly by another formula if the diagonal is known.
The diagonal (d) of a cube is given as, d = 3s, where, 's' is the side length of the cube. From this formula, we can write 's' as, s = d/√3.
By substituting this in the above formula (V = s3), we get:
V = (d/√3)3 = d3/(3√3)
By rationalizing the denominator:
V = (√3d3)/9
Thus, the volume of a cube equation using diagonal can finally be given as:
Volume of the cube = (√3×d3)/9, where d is the length of the diagonal of the cube.
Note: A common mistake is to be avoided by not confusing the diagonal of a cube with the diagonal of its face. The diagonal of a cube cut through its center, as shown in the figure above. While the face diagonal is the diagonal on each face of the cube.
How To Find the Volume of a Cube?
The volume of a cube can be easily found out by just knowing the length of its edge or the measure of its diagonal. Different steps to be followed to calculate the area of the cube depending upon the given parameters will be covered in this section.
Finding Volume of Cube Given Edge Length
The measure of all the sides of a cube is the same thus, we only need to know one side in order to calculate the volume of the cube. The steps to calculate the volume of a cube using the side length are,
- Step 1: Note the measurement of the side length of the cube.
- Step 2: Apply the formula to calculate the volume using the side length: Volume of cube = (side)3.
- Step 3: Express the final answer along with the unit (cubic units) to represent the obtained volume.
Example: Calculate the volume of a cube with a side length of 2 inches.
Solution: The volume of a cube with a side length of 2 inches would have a volume of (2 × 2 × 2) = 8 cubic inches.
Thus, it can hold a total of 8 cubes of 1 inch each. The same can be understood with the help of the given diagram.
Calculating Volume of Cube Given Diagonal
Given the diagonal, we can follow the steps given below in order to find the volume of a given cube.
- Step 1: Note the measurement of the diagonal of the given cube.
- Step 2: Apply the formula to find the volume using diagonal: [√3×(diagonal)3]/9
- Step 3: Express the obtained result in cubic units.
Example: Find the volume of a cube with the diagonal measuring 3 in.
Given: Diagonal = 9 in
We know, volume of cube = [√3×(diagonal)3]/9
⇒ Volume = [√3×(3)3]/9 = 3 × √3 = 3 × 1.732 = 5.196 in3.
Important Notes on Volume of Cube:
The formulas to find the volume of a cube are:
- V = s3, where s is the edge length of the cube.
- V = √3×d3/9, where d is the diagonal length of the cube.
- If the side dimensions of the two cubes are 8 inches and 12 inches, how many small cubes can fit in the larger one?
- Why will the ratio of the volume of two cubes with side lengths in the ratio of 1:2 be 1:8?
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Volume of Cube Examples
Example 1: Using the volume of a cube formula, calculate the side length of a Rubik's cube whose volume is 64 in3.
Solution: To find: Length of the cube (s) = 4 inches
Given: Volume of Rubik's cube = 64 in3
Using the volume of cube formula,
Volume of the cube = s3, where 's' is the side length.
Putting the values, we get,
⇒ 64 = (s3)
⇒ s = (64)1/3 = 4 in
Answer: Side length of the Rubik's cube = 4 in.
Example 2: Find the volume of a cube if the length of its diagonal is 12 inches?
Solution: To find: Volume of cube
Given: Diagonal of the cube = 12 in.
The volume of the cube equation when diagonal is given is:
Volume of cube = (√3×d3)/9
⇒ Volume of given cube = (√3×123)/9 = 332.553 in3
Answer: Volume of the cube = 332.553 in3
Example 3: A cube with an edge length of 6 cm and a cuboid with dimensions 6 cm × 5 cm × 8 cm are on a table. Which shape has more volume?
The volume of the cube = 63 = 216 cm3.
The volume of the cuboid = 6 cm × 5 cm × 8 cm = 240 cm3
Answer: Cuboid has more volume.
Practice Questions on Volume of Cube
FAQs on Volume of Cube
What is the Definition of Volume of Cube?
The volume of a cube is defined as the total space enclosed by the cube in a three-dimensional space. It represents the total number of cubic units completely occupied by the cube. The volume of a cube helps in determining the capacity of a cubical-shaped object.
What Is the Formula for the Volume of a Cube?
The volume of a cube is obtained by multiplying its side three times. The formula of volume of the cube can thus be given as, Volume of cube = s3, where s is the side length of the cube.
How To Calculate the Volume of the Cube?
To calculate the volume of a cube, we either need the measurement of its side length or the length of its diagonal.
- To find the volume using the side length of a cube, we multiply the side three times.
- In order to calculate a cube's volume using diagonal, we can apply the formula: (√3×d3)/9, where d is the length of the cube's body diagonal.
What Is the Unit of Volume of the Cube?
The unit of volume of a cube is given as the cubic units or (unit)3. Also, the SI unit of volume is the cubic meter (m3 ), which is the volume occupied by a cube with each side measuring 1m. Some other important units are cubic feet(ft3), cubic centimeters(cm3), cubic millimeters(mm3), cubic inches(in3), cubic yards(yd3), etc.
What are the Formulas for Finding the Volume of Cube Cuboid and Cylinder?
- The volume of cube = (side)3
- The volume of cuboid = length × width × height
- The volume of cylinder = π(radius)2(height)
How To Find the Side of a Cube When Given the Volume?
The volume of a cube equation using its side is as V = side × side × side or (side)3. This formula can be rearranged to calculate the side length as side = ∛V. Here, the symbol ∛ stands for cube root.
What Is the Volume of Cube With Side 1 Meter?
To find the volume of a cube, we find the cube of its side length. The volume of a cube with the side measuring 1 meter = (1)3 m3 = 1 m3. This value represents the total space enclosed by the given cube.
How to Find Volume of Cube Using Calculator?
Volume of a cube can be easily and quickly determine with the help of the volume of a cube calculator. It is an online tool that helps children to do the calculation with accuracy and get the answers within seconds. To find the volume of a cube using a calculator we required sufficient data or the value of certain parameters such as measurement of the edge of a cube. Try Cuemath's volume of a cube calculator and get your answers just by a click.
☛Check volume of cubes worksheets now for more practice.
How To Find Volume of Cube If Diagonal is Given?
To find the volume of a cube, given the diagonal, we can apply the formula: (√3×d3)/9, where d is the length of the cube's body diagonal. Remember that this formula is applicable when the length of the body diagonal is given and not the face diagonal.