Question

The length of a cube is increased by 20%. What is the percentage change in volume?

Answer 1

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

1. **Initial volume of the cube:** Let's denote the initial length of the cube as \( L \). The volume \( V \) of a cube is given by the formula:
\[
V = L^3
\]

2. **New length after the increase:** If the length is increased by 20%, the new length \( L' \) is:
\[
L' = L + 0.20L = 1.20L
\]

3. **New volume with the increased length:** The new volume \( V' \) with the new length is:
\[
V' = (L')^3 = (1.20L)^3 = 1.20^3L^3
\]
Now, we calculate \( 1.20^3 \):
\[
1.20^3 = 1.20 \times 1.20 \times 1.20 = 1.728
\]
Therefore, the new volume is:
\[
V' = 1.728L^3
\]

4. **Calculate the volume change:** The change in volume is:
\[
\Delta V = V' - V = 1.728L^3 - L^3 = (1.728 - 1)L^3 = 0.728L^3
\]

5. **Percentage change in volume:** The percentage change in volume can be calculated using the formula:
\[
\text{Percentage Change} = \left( \frac{\Delta V}{V} \right) \times 100 = \left( \frac{0.728L^3}{L^3} \right) \times 100 = 0.728 \times 100 = 72.8\%
\]

Thus, the percentage change in volume is **72.8%**.