Find the total surface area (in `cm^(2)`) of a cube of side 7.5 cm.

Options

A. `364.5`
B. 446
C. `337.5`
D. 684

Answer

To find the total surface area of a cube with a side length of 7.5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for the total surface area of a cube**:
The total surface area (TSA) of a cube is given by the formula:
\[ \text{TSA} = 6a^2 \]
where \( a \) is the length of one side of the cube.

2. **Substitute the value of the side length**:
Here, the side length \( a \) is given as 7.5 cm. So, we substitute this value into the formula:
\[ \text{TSA} = 6 \times (7.5)^2 \]

3. **Calculate \( (7.5)^2 \)**:
First, we need to calculate \( 7.5^2 \):
\[ 7.5 \times 7.5 = 56.25 \]

4. **Multiply by 6**:
Now, we multiply the result by 6 to find the total surface area:
\[ \text{TSA} = 6 \times 56.25 = 337.5 \]

5. **State the final answer**:
Therefore, the total surface area of the cube is:
\[ \text{TSA} = 337.5 \, \text{cm}^2 \]

### Final Answer:
The total surface area of the cube is \( 337.5 \, \text{cm}^2 \).