The edge of a cube is increased by `100%` , the surface area of the cube is increased by :

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem of how much the surface area of a cube increases when its edge is increased by 100%, we can follow these steps:

### Step 1: Understand the initial conditions
Let the original edge length of the cube be \( a \). For simplicity, we can assume \( a = 1 \).

### Step 2: Calculate the original surface area
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]
Substituting \( a = 1 \):
\[ S = 6 \times 1^2 = 6 \]

### Step 3: Determine the new edge length after a 100% increase
A 100% increase in the edge length means the new edge length \( a' \) is:
\[ a' = a + 100\% \text{ of } a = a + a = 2a \]
Substituting \( a = 1 \):
\[ a' = 2 \times 1 = 2 \]

### Step 4: Calculate the new surface area
Now, we calculate the new surface area \( S' \) using the new edge length:
\[ S' = 6(a')^2 = 6(2)^2 = 6 \times 4 = 24 \]

### Step 5: Calculate the increase in surface area
To find the increase in surface area, we subtract the original surface area from the new surface area:
\[ \text{Increase} = S' - S = 24 - 6 = 18 \]

### Step 6: Calculate the percentage increase
To find the percentage increase in surface area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{S} \right) \times 100 = \left( \frac{18}{6} \right) \times 100 = 300\% \]

### Final Answer
The surface area of the cube is increased by **300%**.

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