If the base of right rectangular prism remains constant and the measures of the lateral edges are halved, then its volume will be redeuced by :

Options

A. `50%`
B. `33.33%`
C. `66.66%`
D. none of these

Answer

To solve the problem, we need to understand the relationship between the dimensions of a right rectangular prism and its volume. The volume \( V \) of a right rectangular prism is given by the formula:

\[ V = \text{Base Area} \times \text{Height} \]

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the base area of the prism be \( A \) (which remains constant).
- Let the original height of the prism be \( h \).

2. **Calculate the Original Volume**:
- The original volume \( V_{\text{original}} \) can be expressed as:
\[ V_{\text{original}} = A \times h \]

3. **Halve the Height**:
- According to the problem, the measures of the lateral edges (which include the height) are halved. Therefore, the new height \( h_{\text{new}} \) is:
\[ h_{\text{new}} = \frac{h}{2} \]

4. **Calculate the New Volume**:
- The new volume \( V_{\text{new}} \) with the halved height is:
\[ V_{\text{new}} = A \times h_{\text{new}} = A \times \left(\frac{h}{2}\right) = \frac{A \times h}{2} \]

5. **Relate the New Volume to the Original Volume**:
- From the above, we can see that:
\[ V_{\text{new}} = \frac{1}{2} \times V_{\text{original}} \]
- This means the new volume is half of the original volume.

6. **Determine the Volume Reduction**:
- The reduction in volume can be calculated as:
\[ \text{Volume Reduction} = V_{\text{original}} - V_{\text{new}} = V_{\text{original}} - \frac{1}{2} V_{\text{original}} = \frac{1}{2} V_{\text{original}} \]

7. **Express the Reduction as a Percentage**:
- The volume is reduced by:
\[ \text{Percentage Reduction} = \frac{\text{Volume Reduction}}{V_{\text{original}}} \times 100\% = \frac{\frac{1}{2} V_{\text{original}}}{V_{\text{original}}} \times 100\% = 50\% \]

### Conclusion:
The volume of the right rectangular prism will be reduced by **50%** when the height is halved while keeping the base area constant.