Calculating Cube Volume from Surface Area

The question asks for the volume of a cube given its surface area. We need to find the side length first using the surface area formula, and then calculate the volume.

Finding the Cube Side Length

The formula for the surface area (SA) of a cube with side length $a$ is:

$ SA = 6a^2 $

We are given that the surface area is $1014 \text{ m}^2$. Let's substitute this value:

$ 1014 \text{ m}^2 = 6a^2 $

Now, solve for $a^2$:

$ a^2 = \frac{1014 \text{ m}^2}{6} $

$ a^2 = 169 \text{ m}^2 $

To find the side length $a$, take the square root:

$ a = \sqrt{169 \text{ m}^2} $

$ a = 13 \text{ m} $

Calculating the Cube Volume

The formula for the volume (V) of a cube with side length $a$ is:

$ V = a^3 $

Substitute the side length we found ($a = 13 \text{ m}$):

$ V = (13 \text{ m})^3 $

$ V = 13 \times 13 \times 13 \text{ m}^3 $

$ V = 169 \times 13 \text{ m}^3 $

$ V = 2197 \text{ m}^3 $

Therefore, the volume of the cube is $2197 \text{ m}^3$. This matches Option B.