Question

If the side lengths of a cube are doubled, how will the surface area of the cube change?

a) The surface area will remain the same.
b) The surface area will increase by a factor of 4.
c) The surface area will increase by a factor of 2.
d) The surface area will increase by a factor of 8.

Answer 1

When the side lengths of a cube are doubled, the surface area of the cube will increase by a factor of four.

Step-by-step explanation:

When the side lengths of a cube are doubled, the surface area of the cube will increase by a factor of four.

To understand why, let's consider a cube with side lengths :

The surface area of the cube is given by the formula: SA = 6s²

If we double the side length to 2s, the new surface area becomes: SA = 6(2s)² = 6(4s²) = 24s²

So, the surface area of the cube is quadrupled when the side lengths are doubled.