If the surface area of cube is 384 `cm^2`, then what is the volume (in `cm^3`) of the cube?

Options

A. A)512
B. B)356
C. C)484
D. D)686

Answer

To find the volume of the cube given its surface area, 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:
\[ SA = 6 \times a^2 \]
where \( a \) is the length of one side of the cube.

### Step 2: Set up the equation with the given surface area.
We know the surface area of the cube is 384 cm². Therefore, we can set up the equation:
\[ 6 \times a^2 = 384 \]

### Step 3: Solve for \( a^2 \).
To isolate \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{384}{6} \]
\[ a^2 = 64 \]

### Step 4: Solve for \( a \).
Now, take the square root of both sides to find the length of one side of the cube:
\[ a = \sqrt{64} \]
\[ a = 8 \, \text{cm} \]

### 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 \( a \):
\[ V = 8^3 \]
\[ V = 512 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 512 \, \text{cm}^3 \).

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