If each edge of a cube is increased by 10% then by how much per cent will be the surface area of this cube be increased ?

Options

A. 0.21
B. 0.18
C. 0.15
D. 0.2

Answer

To solve the problem of how much the surface area of a cube increases when each edge is increased by 10%, we can follow these steps:

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

### Step 2: Calculate the original surface area
The formula for the surface area \( S \) of a cube is given by:
\[ S = 6a^2 \]
So, the original surface area is:
\[ S_{\text{original}} = 6a^2 \]

### Step 3: Calculate the new edge length after a 10% increase
If each edge is increased by 10%, the new length of each edge \( a' \) is:
\[ a' = a + 0.1a = 1.1a \]

### Step 4: Calculate the new surface area
Now, we can calculate the new surface area \( S' \) using the new edge length:
\[ S' = 6(a')^2 = 6(1.1a)^2 = 6 \times 1.21a^2 = 7.26a^2 \]

### Step 5: Calculate the increase in surface area
The increase in surface area \( \Delta S \) is:
\[ \Delta S = S' - S_{\text{original}} = 7.26a^2 - 6a^2 = 1.26a^2 \]

### Step 6: Calculate the percentage increase in surface area
To find the percentage increase, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta S}{S_{\text{original}}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{1.26a^2}{6a^2} \right) \times 100 = \left( \frac{1.26}{6} \right) \times 100 = 21\% \]

### Conclusion
Thus, the surface area of the cube will increase by **21%** when each edge is increased by 10%.

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