Question

the square area of a cube is the product of 6 and the of the side length . How does the surface area of a cube change when the side of a cube doubles in length

Answer 1

By formula,

The change in length will result in a (change)² of the area.

For example, when the length is increased to 2 times, the area will be increased to 2² = 4 times.

To prove:

Let the length of the side of the cube = x

When the length is double, the length = 2x

Surface area when the length is x:

one face = x²

Total surface area = 6x²

Surface area when the length is 2x:

one face =  (2x)² = 4x²

Surface area = 6(4x²) = 24x²

Find the number of times it increased:

Number of times it increased = 24x²/6x² = 4

Answer: The area will increased by 4 times when the length of the side increased by 2 times.