Answer:
1. The volume of cube is ![\frac{8}{27} \ cubic\ units.](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B27%7D%20%5C%20cubic%5C%20units.)
2. The edge length of cube is ![\frac{3}{4} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%5C%20units.)
3. The side length of square is ![\frac{1}{4} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%5C%20units.)
Step-by-step explanation:
Given:
1. A cube with edge lengths of 2/ 3 units.
2. A cube with volume 27 /64 cubic units.
3. A square with area 1/ 16 square units.
Now, to get the volume and edge length of cube and side length of square.
1. So, to get the volume we put formula:
Edge = ![\frac{2}{3} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%5C%20units.)
![Volume=(edge)^3](https://tex.z-dn.net/?f=Volume%3D%28edge%29%5E3)
![Volume=(\frac{2}{3} )^3\\\\Volume=\frac{8}{27} \ cubic\ units.](https://tex.z-dn.net/?f=Volume%3D%28%5Cfrac%7B2%7D%7B3%7D%20%29%5E3%5C%5C%5C%5CVolume%3D%5Cfrac%7B8%7D%7B27%7D%20%5C%20cubic%5C%20units.)
2. Now, to get the edge length of cube we put formula:
Volume = ![\frac{27}{64} \ cubic\ units.](https://tex.z-dn.net/?f=%5Cfrac%7B27%7D%7B64%7D%20%5C%20cubic%5C%20units.)
![Volume=(edge)^3](https://tex.z-dn.net/?f=Volume%3D%28edge%29%5E3)
![\frac{27}{64}=(edge)^3\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B27%7D%7B64%7D%3D%28edge%29%5E3%5C%5C%5C%5C)
<em>Using cube root on both sides we get:</em>
![\frac{3}{4} =edge\\\\Edge=\frac{3}{4} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%3Dedge%5C%5C%5C%5CEdge%3D%5Cfrac%7B3%7D%7B4%7D%20%5C%20units.)
3. Now, to get the side length of square we put formula:
Area = ![\frac{1}{16} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D%20%5C%20units.)
![Area= (side)^2](https://tex.z-dn.net/?f=Area%3D%20%28side%29%5E2)
![(\frac{1}{16} )=(side)^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B16%7D%20%29%3D%28side%29%5E2)
<em>Using square root on both sides we get:</em>
![\frac{1}{4} =side](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%3Dside)
![Side=\frac{1}{4} \ units.](https://tex.z-dn.net/?f=Side%3D%5Cfrac%7B1%7D%7B4%7D%20%5C%20units.)
Therefore, 1. the volume of cube is ![\frac{8}{27} \ cubic\ units.](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B27%7D%20%5C%20cubic%5C%20units.)
2. the edge length of cube is ![\frac{3}{4} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%5C%20units.)
3. the side length of square is ![\frac{1}{4} \ units.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%5C%20units.)