If all the dimensions of a cuboid are increased by 100%, by what per cent does the volume of cuboid increase ?

Answer

To solve the problem of how much the volume of a cuboid increases when all its dimensions are increased by 100%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the dimensions of the cuboid**:
Let the original dimensions of the cuboid be \( x \), \( y \), and \( z \).

2. **Calculate the original volume**:
The volume \( V \) of a cuboid is given by the formula:
\[ V = x \times y \times z \]

3. **Increase the dimensions by 100%**:
Increasing each dimension by 100% means that each dimension will double. Therefore, the new dimensions will be:
\[ x' = 2x, \quad y' = 2y, \quad z' = 2z \]

4. **Calculate the new volume**:
The new volume \( V' \) with the increased dimensions will be:
\[ V' = x' \times y' \times z' = (2x) \times (2y) \times (2z) = 8xyz \]

5. **Find the increase in volume**:
The increase in volume is given by:
\[ \text{Increase in Volume} = V' - V = 8xyz - xyz = 7xyz \]

6. **Calculate the percentage increase in volume**:
The percentage increase in volume can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Volume}}{\text{Original Volume}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Increase} = \left( \frac{7xyz}{xyz} \right) \times 100 = 700\% \]

### Final Answer:
The volume of the cuboid increases by **700%** when all its dimensions are increased by 100%.