Question

By what factor does the volume of a cube increase of the lengths of the edges are doubled?

Answer 1

volume increases by a factor of 8

Step-by-step explanation:

the volume (V) of a cube is calculated as

V = s³ ( s is the side length )

if s is doubled to 2s , then

V = (2s)³ = 2s × 2s × 2s = 8s³

That is the volume increases by a factor of 8

Answer 2

The volume of a cube increases by a factor of eight when the lengths of the edges are doubled.

Step-by-step explanation:

The volume of a cube is calculated by cubing the edge length. So, if the lengths of the edges are doubled, we need to calculate the new volume. Let's assume the original volume is V. The new volume will be (2L)³ = 8V. Therefore, the volume of the cube increases by a factor of eight when the lengths of the edges are doubled.

The student has asked about the change in the volume of a cube when the lengths of its edges are doubled. Since the volume of a cube (V) is the cube of the edge length (L), expressed as V = L³, when we double the edge length, the new volume V' becomes (2L)³ which is 8 times the original volume, because (2³) = 8.

Therefore, the volume of the cube increases by a factor of eight when the lengths of the edges are doubled.