If the side of a cube is increased by 20%, then what will be the percentage increase in the volume of cube?

Options

A. 60
B. 66.6
C. 72.8
D. 68.5

Answer

To find the percentage increase in the volume of a cube when the side is increased by 20%, we can follow these steps:

### Step 1: Understand the formula for the volume of a cube
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of a side of the cube.

### Step 2: Calculate the original volume
Let the original side length of the cube be \( a \). Therefore, the original volume \( V_1 \) is:
\[ V_1 = a^3 \]

### Step 3: Calculate the new side length after the increase
If the side length is increased by 20%, the new side length \( a' \) can be calculated as:
\[ a' = a + 0.2a = 1.2a \]

### Step 4: Calculate the new volume
Now, we can find the new volume \( V_2 \) using the new side length:
\[ V_2 = (a')^3 = (1.2a)^3 \]
Calculating this gives:
\[ V_2 = 1.2^3 \cdot a^3 = 1.728a^3 \]

### Step 5: Calculate the increase in volume
The increase in volume \( \Delta V \) is given by:
\[ \Delta V = V_2 - V_1 = 1.728a^3 - a^3 = (1.728 - 1)a^3 = 0.728a^3 \]

### Step 6: Calculate the percentage increase in volume
The percentage increase in volume can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta V}{V_1} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{0.728a^3}{a^3} \right) \times 100 = 0.728 \times 100 = 72.8\% \]

### Final Answer
The percentage increase in the volume of the cube when the side is increased by 20% is **72.8%**.

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