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

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?

Solution:

Let $a$ be the length of the edge of a cube.

Volume of the cube $=a^{3}$

Total surface area $=6 a^{2}$

If the length is doubled, then the new length becomes $2 a$.

Now, new volume $=(2 a)^{3}=8 a^{3}$

Also, new surface area $=6(2 a)^{2}=6 \times 4 a^{2}=24 a^{2}$

$\therefore$ The volume is increased by a factor of 8 , while the surface area increases by a factor of 4 .

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