If each edge of a cube is increased by 40%, the percentage increase in its surface area is

Options

A. `40%`
B. `60%`
C. `80%`
D. `96%`

Answer

To solve the problem of finding the percentage increase in the surface area of a cube when each edge is increased by 40%, we can follow these steps:

### Step 1: Understand the dimensions of the cube
Let the original length of each edge of the cube be \( a \).

### Step 2: Calculate the new edge length after the increase
If each edge is increased by 40%, the new edge length \( a' \) can be calculated as:
\[ a' = a + 0.4a = 1.4a \]

### Step 3: Calculate the original surface area of the cube
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]

### Step 4: Calculate the new surface area after the increase
The new surface area \( S' \) of the cube with the new edge length \( a' \) is:
\[ S' = 6(a')^2 = 6(1.4a)^2 = 6 \times 1.96a^2 = 11.76a^2 \]

### Step 5: Calculate the increase in surface area
The increase in surface area \( \Delta S \) is given by:
\[ \Delta S = S' - S = 11.76a^2 - 6a^2 = 5.76a^2 \]

### Step 6: Calculate the percentage increase in surface area
The percentage increase in surface area can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta S}{S} \right) \times 100 = \left( \frac{5.76a^2}{6a^2} \right) \times 100 \]
\[ = \left( \frac{5.76}{6} \right) \times 100 = 96\% \]

### Final Answer
The percentage increase in the surface area of the cube is **96%**.

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