If the surface area of cube is `294 cm^(2)`, then what is the volume (in `cm^(3)`) of the cube ?

Options

A. 343
B. 512
C. 379
D. 313

Answer

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

### Step 1: Understand the formula for the surface area of a cube.
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]
where \( a \) is the length of a side of the cube.

### Step 2: Set up the equation using the given surface area.
We know from the problem that the surface area is \( 294 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 294 \]

### Step 3: Solve for \( a^2 \).
To isolate \( a^2 \), divide both sides of the equation by \( 6 \):
\[ a^2 = \frac{294}{6} \]
Calculating the right side:
\[ a^2 = 49 \]

### Step 4: Solve for \( a \).
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{49} = 7 \, \text{cm} \]

### Step 5: Calculate the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 7^3 = 343 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 343 \, \text{cm}^3 \).

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