If each edge of a cube is doubled, then find how many times the volume would be increased.

Given: Each edge of a cube is doubled.

To do: To find how many times the volume would be increased.

Solution:

Let $a$ be the side of cube. 

$\therefore$ Volume of the cube$=a^3$

When we double the side of the of the cube, it becomes $2a$.

$\Rightarrow$ Volume of new cube$=( 2a)^3=8a^3$

$\Rightarrow \frac{Volume\ of\ new\ cube}{Volume\ of\ the cube}=\frac{8a^3}{a^3}$

$\Rightarrow \frac{Volume\ of\ new\ cube}{Volume\ of\ the cube}=\frac{8}{1}$

Thus, volume of the cube increase $8$ times, when we double the side of the cube.

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Updated on: 10-Oct-2022

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