If the edse of a cube is halved, then its volume reduces- to________ times the actual volume.

Options

A. `1/3`
B. `1/4`
C. `1/8`
D. `1/2`

Answer

To solve the problem, we need to determine how the volume of a cube changes when its edge length is halved. Here’s a step-by-step solution:

### Step 1: Define the edge length of the cube
Let the edge length of the cube be \( x \).

### Step 2: Calculate the actual volume of the cube
The volume \( V \) of a cube is given by the formula:
\[ V = \text{edge}^3 = x^3 \]
So, the actual volume of the cube is \( x^3 \).

### Step 3: Halve the edge length
If the edge length is halved, the new edge length becomes:
\[ \text{New edge} = \frac{x}{2} \]

### Step 4: Calculate the new volume of the cube
Now, we calculate the volume of the cube with the new edge length:
\[ \text{New Volume} = \left(\frac{x}{2}\right)^3 = \frac{x^3}{2^3} = \frac{x^3}{8} \]

### Step 5: Determine the ratio of the new volume to the actual volume
Now, we find how the new volume compares to the actual volume:
\[ \text{Ratio} = \frac{\text{New Volume}}{\text{Actual Volume}} = \frac{\frac{x^3}{8}}{x^3} = \frac{1}{8} \]

### Conclusion
Thus, when the edge of the cube is halved, its volume reduces to \( \frac{1}{8} \) times the actual volume.

### Final Answer
The volume reduces to \( \frac{1}{8} \) times the actual volume.

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