What will happen to the volume of a cube if its length is doubled?

Cube is a three-dimensional shape that is associated with a certain occupied volume. It has six square faces, each of which corresponds to an equal length. It can be considered to be square sheets stacked together. Also known as a regular hexahedron, it is one of the five platonic solid shapes.

Volume of cube

The volume of a cube is a three-dimensional shape that occupies a certain volume of mass or space. 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). 

Volume of Cube Using 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: Take a noting of the edge length of the cube, say side.
• Step 2: Now, Volume of cube = (side)³.
• Step 3: The final answer is measured along with the cubic units.

Volume of Cube Formula

Volume of the cube = Side × Side × Side = Side³

What will happen to the volume of a cube if its length is doubled?

Solution: 

Volume of the cube = Side³

Since,

All the sides of the cube are equal

Then if the length of a side of the cube is increased 

So, the side of the cube becomes

Side of the cube = 2 × Side

Assume

Side of the cube be ‘s’

Side of the cube = 2s

Now,

Volume of the cube = 2s × 2s × 2s

Volume of the cube = (2s)³

Volume of the cube = 8s³

To find how many times the volume of the cube is increased

⇒  

⇒ 8s³/ s³

⇒ 8

Therefore,

If the length of the cube is doubled then its volume is increased by 8 times.

Sample Questions

Question 1. What will happen if the side of the cube is decreased to half?

Solution:

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Assume the side of the cube be ‘s’

Volume of the cube = s³

According to the question

The side of the cube is decreased to half

Therefore,

Side of the cube = s/2

Now,

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of the decreased side cube = s/2 × s/2 × s/2

Volume of the decreased side cube = (s/2)³

Volume of the decreased side cube = s³/8

Therefore,

If we decrease the side of the cube to half then its volume is decreased by 8 times.

Question 2. If the side of the cube is tripled how many times the volume of the cube will be increased?

Solution:

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Assume the side of the cube be ‘s’

Volume of the cube = s³

According to the question

The side of the cube is increased by 3 times

Therefore,

Side of the cube = 3 × s

Now,

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of the decreased side cube = 3s × 3s × 3s

Volume of the decreased side cube = (3s)³

Volume of the decreased side cube = 27s³

Therefore,

If we increase the side of the cube to 3 times then its volume is increased by 27 times.

Question 3. Calculate the decrease in the volume of the cube if its side is decreased to 1/4?

Solution:

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Assume the side of the cube be ‘s’

Volume of the cube = s³

According to the question

The side of the cube is decreased to 1/4

Therefore,

Side of the cube = s/4

Now,

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of the decreased side cube = s/4 × s/4 × s/4

Volume of the decreased side cube = (s/4)³

Volume of the decreased side cube = s³/64

Therefore,

If we decrease the side of the cube by 1/4 then its volume decreases by 64 times.

Question 4. Find how many small cubes of side 2 cm can be made from a big cube of side 8 cm?

Solution:

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of small cube = 2 × 2 × 2

Volume of small cube = 8 cm³

Volume of big cube = 8 × 8 × 8

Volume of big cube = 512 cm³

To find how many small cubes can be made out of big cube

⇒ 

⇒ 512/8

⇒ 64

Therefore,

64 small cubes of side 2 cm can be made out of a big cube of side 8 cm.