what is the length of a diagonal of a cube whose edge is 6?

Question

answer with solution pls

Answer 1

Length of edge of cube = a.
Diagonal of 1 face using Pythagoras' theorem = b = SQRT(a^2 + a^2) = a.SQRT(2)
Diagonal of cube = SQRT(2a^2 + a^2) = a.SQRT(3)
If Length of edge = 6 then diagonal of cube = 6.SQRT(3) ~10.39

Answer 2

I'll address the general case, imagine a square with sides of length a, then by Pythagoras theorem the diagonal is aV2,
Now picture this diagonal to form along with an edge of length a a right angle. If we construct the triangle we find that the hypotenuse of this triangle is the diagonal of a cube, applying Pythagoras theorem again we find that the length required is,
aV(2+1) = aV3
Your problem has a solution when this general case is reduced to a=6

Answer 3

An edge of the cube is 6, so the diagonal must be 6sqrt(2) units.

(length of face diagonal)^2 = (length of side)^2 + (length of side)^2 (Pythagoran theorem)
= (6 units)^2 + (6 units)^2
= 36 sq. units + 36 sq. units
= 72 sq. units
length of face diagonal = sqrt (72 sq units)
= sqrt (72) units
= sqrt (2 * 36) units
= 6 sqrt(2) units

Now, consider the diagonal of the cube itself.

The diagonal of a cube comes from a right triangle....

Therefore, (diagonal of the cube)^2 = (side of a cube)^2 + (face diagonal)^2 (Pythagoran theorem)
= (6 units)^2 + (6 sqrt(2) units)^2
= 36 sq. units + 72 sq. units
= 108 sq. units
diagonal of the cube = sqrt (108 sq. units)
= sqrt (108) units
= sqrt (3*36) units
= 6 sqrt(3) units

The exact answer is 6 sqrt(3) units, and plugging it in a calculator, you get 10.3923 units, to the nearest four decimal places.

Answer 4

This is a problem that can be solved using vectors. This sounds like a problem from calculus. Using a 3-D coordinate system draw a cube with a a bottom corner touching the point (0,0,0). Make all the sides a length of six. Calculate the vector from the origin to the diagonal edge of cube. The vector is
<6,6,6>. Find the magnitude of this vector. 10.39. Problem solved.

Answer 5

The diagonal of a face of this cube: sq root of 72.....(6^2+6^2=c^2)

The diagonal of two opposite angles in this cube:72+36=c^2

sq rt of 108=the diagonal of two opposite angles in this cube or about 10.3923...

Answer 6

length of the diagonal = length of a side * SQRT(3)
So


Length of the diagonal = 6 * sqrt(3)
= 6 * 1.732
= 10.392 unit

Answer 7

6 time sqrt of 3

Answer 8

use pythagorean
diagonal of a single face is sqrt(2(6^2))
=sqrt(2(36))=sqrt(72)
digonal of the cube is
=sqrt(6^2+sqrt(72)^2)
=sqrt(36+72)=sqrt(108)
=10.39

Answer 9

6*(3)^(1/2)