the area of the cube when the cornor to cornor diagignol is 6 cm?

Answer 1

The diagonal of a cube is the hypotenuse of a right triangle with one leg equal to an edge of the cube and the other leg equal to the diagonal of one of its faces. If the edge of the cube is x, then the face diagonal is x sqrt 2. Use Pythagorean Thm:

x^2 + (x sqrt 2)^2 = 6^2

x^2 + 2x^2 = 36 = 3x^2

x^2 = 12, which is the area of one face. There are 6 faces so the total (surface) area is 72 cm^2

Answer 2

If you are trying to find the volume, I did a little figuring. I came up with the volume of the cube equaling = ( sqrt [ (z^2) / 3 ] )^3, where z is the length of the diagonal from the top corner, to the opposite corner.

^ = take the power of

Hope this helps.

P.S. That comes out to 24 * sqrt(3)

Answer 3

There is no such thing as the area of a cube, unless you mean surface area. Also I've never heard of a CORNOR.

Answer 4

What the hell is a "cornor diagignol"? I have never heard of a diagignol.

Would three of them be a "trigignol"? Is one of them just a "gignol"? Or would that be a "monogignol"?

Answer 5

Hi. Yeah, yeah, and it's diagonal too. You need to understand coordinates. The formula for a cube's diagonal is based on 3D trig. x^2 + y^2 + z^2 = Diagonal d^2 where x,y, and z are equal in a cube. This should get you started.

Answer 6

108 is the surface area.

If you use the a^2+b^2=c^2, the length of one of the egdes of the cube is the square root of 18, square that and you get the surface area of one side, 18. Multiply that by 6 and you have the entire surface area, 108.

Answer 7

d = a sqrt(3)

6 = a * sqrt(3)
a = 6/(sqrt(3))
a = (6sqrt(3))/3
a = 2sqrt(3)

If by area, you mean volume, then

V = a^3
V = (2sqrt(3))^3
V = 8sqrt(27)
V = 8sqrt(9 * 3)
V = 24sqrt(3)cm^3

but if you want the Total Surface Area, then

T = 6a^2
T = 6(2sqrt(3))^2
T = 6(4 * 3)
T = 6 * 12
T = 72 cm^2