The lateral surface area of a cube is `256cm^(2)`. Find its volume.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the formula for the lateral surface area of a cube.
The lateral surface area (LSA) of a cube is given by the formula:
\[ \text{LSA} = 4s^2 \]
where \(s\) is the length of one side of the cube.

### Step 2: Set up the equation using the given lateral surface area.
We know from the problem that the lateral surface area is \(256 \, \text{cm}^2\). Therefore, we can set up the equation:
\[ 4s^2 = 256 \]

### Step 3: Solve for \(s^2\).
To isolate \(s^2\), divide both sides of the equation by 4:
\[ s^2 = \frac{256}{4} \]
\[ s^2 = 64 \]

### Step 4: Find the value of \(s\).
Now, take the square root of both sides to find \(s\):
\[ s = \sqrt{64} \]
\[ s = 8 \, \text{cm} \]

### Step 5: Calculate the volume of the cube.
The volume \(V\) of a cube is given by the formula:
\[ V = s^3 \]
Substituting the value of \(s\):
\[ V = 8^3 \]
\[ V = 512 \, \text{cm}^3 \]

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

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