Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

To determine the percentage increase in the surface area of a cube when each edge is increased by 50%, we can follow these steps:

Initial Surface Area Calculation

The surface area (SA) of a cube is calculated using the formula:

SA = 6a²

where a is the length of an edge of the cube.

New Edge Length

If the edge length is increased by 50%, the new edge length becomes:

New edge length = a + 0.5a = 1.5a

New Surface Area Calculation

Now, we can find the new surface area using the updated edge length:

New SA = 6(1.5a)²

This simplifies to:

New SA = 6(2.25a²) = 13.5a²

Calculating the Increase

The increase in surface area is:

Increase = New SA - Original SA

Increase = 13.5a² - 6a² = 7.5a²

Percentage Increase

To find the percentage increase, we use the formula:

Percentage Increase = (Increase / Original SA) × 100

Substituting the values:

Percentage Increase = (7.5a² / 6a²) × 100 = 125%

Thus, the percentage increase in the surface area of the cube is 125%.