Respuesta :
Given:
Volume of Large cube = 1 cubic unit
Volume of small cube = [tex]\dfrac{1}{27}[/tex] 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 [tex]a_1[/tex] and [tex]a_2[/tex] respectively.
We know that, volume of a cube is
[tex]V=(edge)^3[/tex]
Volume of Large cube = 1 cubic unit
[tex](a_1)^3=1[/tex]
Taking cube root on both sides, we get
[tex]a_1=1[/tex]
So, edge of large cube is 1 unit.
Volume of small cube = [tex]\dfrac{1}{27}[/tex] cubic unit
[tex](a_2)^3=\dfrac{1}{27}[/tex]
Taking cube root on both sides, we get
[tex]a_2=\dfrac{1}{3}[/tex]
So, edge of large cube is [tex]\dfrac{1}{3}[/tex] unit.
Now, difference between them is
[tex]d=a_1-a-2[/tex]
[tex]d=1-\dfrac{1}{3}[/tex]
[tex]d=\dfrac{3-1}{3}[/tex]
[tex]d=\dfrac{2}{3}[/tex]
Therefore, the difference between the edge length of the large cube and the edge length of the small cube is [tex]\dfrac{2}{3}[/tex] unit.
