If each side of a cube is increased by `30%` then find the change in surface area?

Options

A. `40%`
B. `38.4%`
C. `35%`
D. `69%`

Explanation

To find the change in surface area of a cube when each side is increased by 30%, we can follow these steps:

### Step 1: Define the original side length
Let the original side length of the cube be \( L_1 = 1 \) cm (for simplicity).

### Step 2: Calculate the original surface area
The surface area \( A_1 \) of a cube is given by the formula:
\[ A_1 = 6L^2 \]
Substituting \( L_1 = 1 \):
\[ A_1 = 6 \times (1)^2 = 6 \text{ cm}^2 \]

### Step 3: Calculate the new side length after a 30% increase
If each side is increased by 30%, the new side length \( L_2 \) can be calculated as:
\[ L_2 = L_1 \times \left(1 + \frac{30}{100}\right) = L_1 \times 1.3 = 1 \times 1.3 = 1.3 \text{ cm} \]

### Step 4: Calculate the new surface area
Now, we calculate the new surface area \( A_2 \) using the new side length \( L_2 \):
\[ A_2 = 6L_2^2 = 6 \times (1.3)^2 \]
Calculating \( (1.3)^2 \):
\[ (1.3)^2 = 1.69 \]
Thus,
\[ A_2 = 6 \times 1.69 = 10.14 \text{ cm}^2 \]

### Step 5: Find the change in surface area
The change in surface area \( \Delta A \) is given by:
\[ \Delta A = A_2 - A_1 = 10.14 - 6 = 4.14 \text{ cm}^2 \]

### Step 6: Calculate the percentage change in surface area
The percentage change in surface area can be calculated using the formula:
\[ \text{Percentage Change} = \left(\frac{\Delta A}{A_1}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left(\frac{4.14}{6}\right) \times 100 \approx 69\% \]

### Conclusion
The change in surface area when each side of a cube is increased by 30% is approximately **69%**.

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