Question

If I have a 1x1x1 cube. How can I make it so it has twice the surface area?

Answer 1

I think 6

Answer 2

well, the surface Area of a cube the dimensions of which are 1, 1, 1 is ?

Answer 3

There are 6 same faces, 1 by 1 each. So if each face has area of 1 (meter squared),
then all of these 6 faces added would give you the (entire surface) area of ?

Answer 4

6

Answer 5

yes, the surface area of a cube whose side (each one) is 1, is 6.

Answer 6

so how do you make it so it is twice that?

Answer 7

Now, how did we obtain this surface area (once again) ?
(I will denote my side as "s" )

\(\large\color{black}{ \displaystyle {\rm A_{~surface~of~a~cube}}~=~6s^2 }\)

do you understand this formula?

Answer 8

(each face is s^2, and there are 6 of these faces )

Answer 9

yes or no ?

Answer 10

yes, so to make it so the surface area is twice as much you square it?

Answer 11

so you have the following for your surface area:
\(\large\color{black}{ \displaystyle {\rm A_{~surface~of~a~cube}}~=~6(1)^2 }\)
which gave you that A=6

Answer 12

but, we need to go backwards.
We want to know how long should each side should be to get a surface area of 12.

Answer 13

\(\large\color{black}{ \displaystyle {\rm 12}~=~6s^2 }\)

Answer 14

Solve for s (and disregard any negative solution if you get it)

Answer 15

so 12/6=2 so \[\sqrt{2}=s ^{2}\]

Answer 16

you mean \(\large\color{black}{ \displaystyle s=\sqrt{2} }\) ?

Answer 17

yea sorry

Answer 18

it is alright, as long as you get it (which you apparently do).

Answer 19

So, to have a surface area of 12 (which is twice more than the surface of 6), you would need each side to be \(\large\color{black}{ \displaystyle \sqrt{2} }\) units long

Answer 20

any questions about this ?

Answer 21

no, thank you for your help

Answer 22

yw