If the edge of a cube is doubled, what happens to its volume?

• A. It remains the same
• B. It doubles
• C. It triples
• D. It increases by a factor of eight

Answer: (D)

To understand what happens to the volume of a cube when its edge is doubled, we start with the formula for the volume of a cube, which is calculated as the cube of the length of one of its edges. If we denote the original length of an edge as ( s ), the volume ( V ) of the cube is given by the formula:

[

V = s^3

]

Now, if the length of the edge is doubled, the new length becomes ( 2s ). We can then calculate the new volume ( V' ) using the same volume formula:

[

V' = (2s)^3

]

Expanding this, we find:

[

V' = 2^3 \cdot s^3 = 8 \cdot s^3

]

This result indicates that the new volume is eight times the original volume:

[

V' = 8V

]

Thus, when the edge of the cube is doubled, the volume increases by a factor of eight. This understanding highlights the relationship between the dimensions of a 3-dimensional shape and its volume, illustrating that when all linear dimensions are scaled by a factor, the volume scales by the cube of