Question

If the length of each side of a cube is halved, is the surface area halved? Use an example to support your answer.

Answer 1

Please help! :)

Answer 2

nope it wouldn't be halved but rather be one fourth of it;
The surface area of a cube = 6a^2
so lets use as the first cube which would be the bigger one that 'a' the side = 4; and the second one a = 2.

So for the first cube;
SA = 6a^2
SA =6(4)^2
SA =6(16)
SA =96

Now for the second one;

SA = 6a^2
SA =6(2)^2
SA =6(4)
SA =24
so lets divide them,
96/24 = 4 so the bigger one is four times the smaller or
24/96 = 1/4 so it represents that the smaller is one fourth of the bigger one.

Another way to solve this is by using the formula;
a^2 4^2 a^2 2^2
--- = --- --- = ---
b^2 2^2 b^2 4^2

a^2 16 a^2 4
--- = --- --- = ---
b^2 4 b^2 16

a^2 4 a^2 1
--- = --- = 4 --- = ---
b^2 1 b^2 4

Again, the four would be if your saying that the bigger one is four times the smaller, and the 1/4 is used for saying that the smaller is one fourth the big one.