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 edge of given cube be $a.$

$\therefore$ Volume of the cube, $V=a^3$

and surface area, $S.A=6a^2$

By doubling the edge of cube, the side of new cube $=a\times 2=2a$

$\therefore$ New Volume $=V^{\prime }=(2a{)}^3=8a^3=8\times a^3$

and, New surface area, $S.A^{\prime }=6(2a{)}^2=6\times 4a^2$

$=24a^2=4\times 6a^2$

It is clear from the above that

$V^{\prime }=8\times V$

and, $S.A^{\prime }=4\times S.A$

Hence, Volume is increased $8$ times and the surface area is $4$ times.