Question

1. What is the volume of a cube with edge lengths of 2/ 3 units? 2. What is the edge length of a cube with volume27 /64 cubic units? 3. Hat is the side length of a square with area 1/ 16 square units?

Answer 1

Answer:

1. The volume of cube is  $\frac{8}{27} \ cubic\ units.$

2. The edge length of cube is  $\frac{3}{4} \ units.$

3. The side length of square is  $\frac{1}{4} \ units.$

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 = $\frac{2}{3} \ units.$

$Volume=(edge)^3$

$Volume=(\frac{2}{3} )^3\\\\Volume=\frac{8}{27} \ cubic\ units.$

2. Now, to get the edge length of cube we put formula:

Volume = $\frac{27}{64} \ cubic\ units.$

$Volume=(edge)^3$

$\frac{27}{64}=(edge)^3$

Using cube root on both sides we get:

$\frac{3}{4} =edge\\\\Edge=\frac{3}{4} \ units.$

3. Now, to get the side length of square we put formula:

Area = $\frac{1}{16} \ units.$

$Area= (side)^2$

$(\frac{1}{16} )=(side)^2$

Using square root on both sides we get:

$\frac{1}{4} =side$

$Side=\frac{1}{4} \ units.$

Therefore, 1. the volume of cube is $\frac{8}{27} \ cubic\ units.$

2. the edge length of cube is $\frac{3}{4} \ units.$

3. the side length of square is $\frac{1}{4} \ units.$