Respuesta :
Answer:
1. The volume of cube is [tex]\frac{8}{27} \ cubic\ units.[/tex]
2. The edge length of cube is [tex]\frac{3}{4} \ units.[/tex]
3. The side length of square is [tex]\frac{1}{4} \ units.[/tex]
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 = [tex]\frac{2}{3} \ units.[/tex]
[tex]Volume=(edge)^3[/tex]
[tex]Volume=(\frac{2}{3} )^3\\\\Volume=\frac{8}{27} \ cubic\ units.[/tex]
2. Now, to get the edge length of cube we put formula:
Volume = [tex]\frac{27}{64} \ cubic\ units.[/tex]
[tex]Volume=(edge)^3[/tex]
[tex]\frac{27}{64}=(edge)^3\\\\[/tex]
Using cube root on both sides we get:
[tex]\frac{3}{4} =edge\\\\Edge=\frac{3}{4} \ units.[/tex]
3. Now, to get the side length of square we put formula:
Area = [tex]\frac{1}{16} \ units.[/tex]
[tex]Area= (side)^2[/tex]
[tex](\frac{1}{16} )=(side)^2[/tex]
Using square root on both sides we get:
[tex]\frac{1}{4} =side[/tex]
[tex]Side=\frac{1}{4} \ units.[/tex]
Therefore, 1. the volume of cube is [tex]\frac{8}{27} \ cubic\ units.[/tex]
2. the edge length of cube is [tex]\frac{3}{4} \ units.[/tex]
3. the side length of square is [tex]\frac{1}{4} \ units.[/tex]
