To solve the problem, we need to find the length of the edge of a cube when given its surface area, and then use this edge length to compute the volume of the cube.
### Step-by-Step Solution:
#### Part (i): Finding the length of the edge
1. Understanding the surface area formula for a cube:
The surface area of a cube is calculated by the formula:
[tex]\[
A = 6 \times \text{edge length}^2
\][/tex]
where [tex]\( A \)[/tex] is the surface area.
2. Given the surface area:
We know the surface area of the cube is [tex]\( 24 \, \text{cm}^2 \)[/tex].
3. Setting up the equation:
Using the formula, we have:
[tex]\[
6 \times \text{edge length}^2 = 24
\][/tex]
4. Solving for the edge length:
- Divide both sides of the equation by 6:
[tex]\[
\text{edge length}^2 = \frac{24}{6} = 4
\][/tex]
- Take the square root of both sides:
[tex]\[
\text{edge length} = \sqrt{4} = 2 \, \text{cm}
\][/tex]
#### Part (ii): Finding the volume of the cube
1. Understanding the volume formula for a cube:
The volume [tex]\( V \)[/tex] of a cube is given by:
[tex]\[
V = \text{edge length}^3
\][/tex]
2. Substituting the edge length:
We found the edge length to be [tex]\( 2 \, \text{cm} \)[/tex].
3. Calculating the volume:
[tex]\[
V = 2^3 = 2 \times 2 \times 2 = 8 \, \text{cm}^3
\][/tex]
### Final Answers:
(i) The length of the edge of the cube is [tex]\( 2 \, \text{cm} \)[/tex].
(ii) The volume of the cube is [tex]\( 8 \, \text{cm}^3 \)[/tex].
