Question

@Igreen @AnswerMyQuestions @lordhelix8th A cube is cut perpendicular to and diagonally across the base, as shown below.
https://assets.edmodo.com/snapshot/nwea/MathGrade-8-6.zip-0/images/149487.jpg

What is the ratio of the area of the shaded cross-section to the area of one of the square faces of the cube?

A. 1 : 1

B. 2√:1

C. 3√:1

D. 2 : 1

Answer 1

Well?

Answer 2

Sorry, my internet just konked out for a second there.

Answer 3

\(\small\color{#AC58FA}{Oh,~Alright~then.}\)

Answer 4

@ganeshie8

Answer 5

I've never seen a question like this before, the diagonal area obviously has to be bigger than the face of one side..which eliminates Option A..

Answer 6

@iambatman @Hero @Kainui

Answer 7

I'm doomed

Answer 8

lol i sure hope not

Answer 9

this cannot be that hard
lets see what we can do

Answer 10

since it doesn't depend on the length of the edge of the cube, we can pick a number for it
the easiest number to pick is 1, so the area of the side of the cube is \(1\times 1=1\)
that was easy enough

Answer 11

then for the area of the shaded region

Answer 12

one of the sides of the shaded region is the edge of the cube which is 1
the other side of the shaded region is the diagonal of the square with edge 1, so it is \(\sqrt2\)

Answer 13

the shaded region then has area \(\sqrt2\times 1=\sqrt2\)

Answer 14

so your ratio is \(\sqrt 2:1\)

Answer 15

that was not so bad was it? better than being doomed

Answer 16

THANK YOU SO SO SO SO MUCH

Answer 17

=\[\frac{ \sqrt{2}}{ 1}\]