Question

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

Answer 1

Let a be the length of the edge of a cube.
Volume of the cube$=a^3$
Total surface area$=6a^2$

If the length is doubled, then the new length becomes 2a.
Now, new volume $=(2a{)}^3=8a^3$
Also, new surface area=$=6(2a{)}^2=6\times 4a^2=24a^2$
∴ The volume is increased by a factor of 8, while the surface area increases by a factor of 4.