The volume of a cube is `343cm^(3)`. Its total surface area is

Options

A. `196cm^(2)`
B. `49 cm^(2)`
C. `294 cm^(2)`
D. `147 cm^(2)`

Answer

To find the total surface area of a cube when given its volume, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the volume of a cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of a side of the cube.

2. **Set the volume equal to the given value**:
We know the volume of the cube is \( 343 \, \text{cm}^3 \). Thus, we can write:
\[ a^3 = 343 \]

3. **Find the side length \( a \)**:
To find \( a \), we need to take the cube root of \( 343 \):
\[ a = \sqrt[3]{343} \]
We can express \( 343 \) as \( 7^3 \):
\[ a = \sqrt[3]{7^3} = 7 \, \text{cm} \]

4. **Use the side length to find the total surface area**:
The total surface area \( A \) of a cube is given by the formula:
\[ A = 6a^2 \]
Now substituting \( a = 7 \, \text{cm} \):
\[ A = 6 \times (7)^2 \]

5. **Calculate \( 7^2 \)**:
\[ 7^2 = 49 \]

6. **Calculate the total surface area**:
Now substituting back into the surface area formula:
\[ A = 6 \times 49 = 294 \, \text{cm}^2 \]

### Final Answer:
The total surface area of the cube is \( 294 \, \text{cm}^2 \).

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