Question

If the dimension of the cube is dubbed, how many times will the volume increase ? ​

Answer 1

Answer:

Whenever a three-dimensional shape is made bigger while remaining similar to itself, in a way that any characteristic length of it (like the edge of a cube, the height of a cylinder, the diameter of a sphere, the perimeter of the base of a cone etc.) is doubled, the volume of the three-dimensional shape is increased 2³ = 8 times.

More generally, if a characteristic length is altered by a factor k, the volume of the three-dimensional shape is altered by a factor of k³.

Another example:

- A sphere has a diameter 20% less than the diameter of a bigger sphere. How much less is its volume?

Answer:

100 % - 20 % = 80 % or 0,8

So,

V₂ = (0,8)³ * V₁ = 0,512 * V₁ or 48,8 % smaller.

Related to the above is the so called Delian problem (Doubling the cube), which is an ancient geometric problem:

Answer 2

Answer:

Condition:-

Dimension is doubled means each side is doubled

Assumption:

Let the side be x

Let the increased side be x

According to question:-

$Volume \: \: of \: \: cube= {x}^{3}$

$Volume \: \: of \: \: increased \: \: side \: \: of \: \: cube = {(2x)}^{3}$

On comparing be get:-

${x}^{3} = {8x}^{3}$

So the volume of the cube will become 8 times the volume of orignal cube.

Lets verify in some sides

Let we take side as 3

Volume of cube will be= 3×3×3

=27

If we double the side so 3 becomes 6

Volume of increased cube=6×6×6

=216

On dividing the two volumes be get 8.

So,hence verified

Similarly take 4

Volume of cube=4×4×4

=64

On doubling 4 becomes 8

Volume of increased side=8×8×8

=512

On dividing we again get 8

Hence,

If we double the side of cube the volume of cube will become 8 times the orignal volume.