Given:
Volume of Large cube = 1 cubic unit
Volume of small cube =
cubic unit
To find:
The difference between the edge length of the large cube and the edge length of the small cube.
Solution:
Let the edges of large and small cubes are
and
respectively.
We know that, volume of a cube is
![V=(edge)^3](https://tex.z-dn.net/?f=V%3D%28edge%29%5E3)
Volume of Large cube = 1 cubic unit
![(a_1)^3=1](https://tex.z-dn.net/?f=%28a_1%29%5E3%3D1)
Taking cube root on both sides, we get
![a_1=1](https://tex.z-dn.net/?f=a_1%3D1)
So, edge of large cube is 1 unit.
Volume of small cube =
cubic unit
![(a_2)^3=\dfrac{1}{27}](https://tex.z-dn.net/?f=%28a_2%29%5E3%3D%5Cdfrac%7B1%7D%7B27%7D)
Taking cube root on both sides, we get
![a_2=\dfrac{1}{3}](https://tex.z-dn.net/?f=a_2%3D%5Cdfrac%7B1%7D%7B3%7D)
So, edge of large cube is
unit.
Now, difference between them is
![d=a_1-a-2](https://tex.z-dn.net/?f=d%3Da_1-a-2)
![d=1-\dfrac{1}{3}](https://tex.z-dn.net/?f=d%3D1-%5Cdfrac%7B1%7D%7B3%7D)
![d=\dfrac{3-1}{3}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7B3-1%7D%7B3%7D)
![d=\dfrac{2}{3}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7B2%7D%7B3%7D)
Therefore, the difference between the edge length of the large cube and the edge length of the small cube is
unit.