If each side of a cube is decreased by 19%, then decrease in surface area is

Options

A. 0.4
B. 0.384
C. 0.35
D. 0.3439

Answer

To solve the problem of finding the decrease in surface area of a cube when each side is decreased by 19%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the decrease in surface area of a cube when each side is decreased by 19%.

2. **Define the Original Side Length**: Let the original side length of the cube be \( s \).

3. **Calculate the New Side Length**: If each side is decreased by 19%, the new side length \( s' \) can be calculated as:
\[ s' = s - 0.19s = 0.81s \]

4. **Calculate the Original Surface Area**: The surface area \( A \) of a cube is given by the formula:
\[ A = 6s^2 \]

5. **Calculate the New Surface Area**: The new surface area \( A' \) after the side length is decreased is:
\[ A' = 6(s')^2 = 6(0.81s)^2 = 6 \times 0.6561s^2 = 3.9366s^2 \]

6. **Calculate the Decrease in Surface Area**: The decrease in surface area \( \Delta A \) can be found by subtracting the new surface area from the original surface area:
\[ \Delta A = A - A' = 6s^2 - 3.9366s^2 = (6 - 3.9366)s^2 = 2.0634s^2 \]

7. **Calculate the Percentage Decrease in Surface Area**: The percentage decrease in surface area is given by:
\[ \text{Percentage Decrease} = \left(\frac{\Delta A}{A}\right) \times 100 = \left(\frac{2.0634s^2}{6s^2}\right) \times 100 \]
Simplifying this gives:
\[ \text{Percentage Decrease} = \left(\frac{2.0634}{6}\right) \times 100 \approx 34.39\% \]

### Final Answer:
The decrease in surface area is approximately **34.39%**.