If the surface area of cube is 294 cm2, then what is the volume (in cm3) 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 (SA) of a cube is given by the formula:
\[ SA = 6a^2 \]
where \( a \) is the length of one side of the cube.

### Step 2: Set up the equation using the given surface area.
Given that the surface area of the cube is 294 cm², 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:
\[ a^2 = \frac{294}{6} \]

### Step 4: Calculate \( a^2 \).
Now, perform the division:
\[ a^2 = 49 \]

### Step 5: Solve for \( a \).
To find \( a \), take the square root of both sides:
\[ a = \sqrt{49} = 7 \text{ cm} \]

### Step 6: Use the side length to find the volume.
The volume (V) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 7^3 \]

### Step 7: Calculate the volume.
Now, calculate \( 7^3 \):
\[ V = 343 \text{ cm}^3 \]

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

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