Find the surface area and the volume of a cube of an edge :
3. 5 cm

Answer

To find the surface area and volume of a cube with an edge length of 3.5 cm, we can follow these steps:

### Step 1: Identify the edge length of the cube
Let the edge length of the cube be denoted as \( a \).
Given:
\[ a = 3.5 \, \text{cm} \]

### Step 2: Calculate the surface area of the cube
The formula for the surface area \( SA \) of a cube is:
\[ SA = 6a^2 \]
Substituting the value of \( a \):
\[ SA = 6 \times (3.5)^2 \]

### Step 3: Calculate \( (3.5)^2 \)
First, calculate \( (3.5)^2 \):
\[ (3.5)^2 = 3.5 \times 3.5 = 12.25 \]

### Step 4: Substitute back to find the surface area
Now substitute \( (3.5)^2 \) back into the surface area formula:
\[ SA = 6 \times 12.25 \]

### Step 5: Calculate \( 6 \times 12.25 \)
Now calculate:
\[ SA = 6 \times 12.25 = 73.5 \, \text{cm}^2 \]

### Step 6: Calculate the volume of the cube
The formula for the volume \( V \) of a cube is:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = (3.5)^3 \]

### Step 7: Calculate \( (3.5)^3 \)
First, calculate \( (3.5)^3 \):
\[ (3.5)^3 = 3.5 \times 3.5 \times 3.5 \]
We already know \( (3.5)^2 = 12.25 \), so:
\[ (3.5)^3 = 12.25 \times 3.5 \]

### Step 8: Calculate \( 12.25 \times 3.5 \)
Now calculate:
\[ 12.25 \times 3.5 = 42.875 \]

### Step 9: Write the final volume
Thus, the volume of the cube is:
\[ V = 42.875 \, \text{cm}^3 \]

### Final Answers:
- Surface Area: \( 73.5 \, \text{cm}^2 \)
- Volume: \( 42.875 \, \text{cm}^3 \)

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