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

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  • Last Updated : 20 Nov, 2021

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

⇒  \frac{Volume\ of\ the\ increased\ length\ cube}{Volume\ of\ the\ initial\ cube}

⇒ 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

⇒ \frac{Volume\ of\ the\ big\ cube}{Volume\ of\ the\ small\ cube}

⇒ 512/8

⇒ 64

Therefore,

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

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