A cube has edge lengths of 6 inches. What is the approximate length of a diagonal "d" of the cube?

A)6 in.
B)8.4 in.
C)10.4 in.
D)12 in.

recall that the diagonal of a cube is given by

d = sqrt(3*s^2)
where s = length of side of cube
substituting,
d = sqrt(3*6^2)
d = sqrt(108)
d = 10.39 = 10.4 in

hope this helps~ :)

THANKS ALOT JAI!!!!! :)

To find the length of the diagonal "d" of a cube, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal "d" of the cube is the hypotenuse, and the sides of the cube are the other two sides.

Let's denote the length of each edge of the cube as "e". In this case, e = 6 inches.

Using the Pythagorean theorem, we have:

d² = e² + e² + e²

Simplifying the equation:

d² = 3e²

Substituting the value of e (6 inches):

d² = 3 * 6²

d² = 3 * 36

d² = 108

Taking the square root of both sides:

d ≈ √108

d ≈ 10.39

Therefore, the approximate length of the diagonal "d" of the cube is 10.39 inches.

The closest answer choice is C) 10.4 inches.

To find the approximate length of the diagonal "d" of a cube, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the case of a cube, the diagonal "d" acts as the hypotenuse of a right-angled triangle.

In a cube, all edges are of equal length. So, in this case, the length of any side of the cube is 6 inches.

Let's label one side of the cube as "s" and the diagonal as "d".

Using the Pythagorean theorem, we have:

d² = s² + s² + s² [since it's a right-angled triangle with three sides of equal length]

d² = 3s²

Substituting the value of "s" (6 inches), we get:

d² = 3(6 in)²

d² = 3(36 in²)

d² = 108 in²

Taking the square root of both sides to find "d", we have:

d ≈ √(108 in²)

d ≈ 10.39 in

Therefore, the approximate length of the diagonal "d" of the cube is 10.39 inches, which is closest to option C) 10.4 in.