A cube has edge lengths of 4 inches. What is the approximate length of a diagonal "d" of the cube?
think of the main diagonal as the hypotenuse of a right triangle, where
the base is the diagonal along the base of the cube, and
the height is the height of the cube.
Now you can see that the main diagonal has length
d = √(4^2+4^2+4^2) = √48
To find the length of the diagonal "d" of a cube with edge length 4 inches, we can use the Pythagorean theorem. The diagonal "d" of the cube can be thought of as the hypotenuse of a right triangle, where the two other sides are the edges of the cube.
For a cube:
- The diagonal "d" is the hypotenuse of a right triangle.
- The other two sides of the right triangle are the edges of the cube, each measuring 4 inches.
Using the Pythagorean theorem, we can calculate the length of the diagonal "d" as follows:
d^2 = a^2 + b^2
where a and b are the lengths of the other two sides.
Plugging in the values:
d^2 = 4^2 + 4^2
Simplifying:
d^2 = 16 + 16
d^2 = 32
Taking the square root of both sides to find "d":
d ≈ √32
Using a calculator, the approximate length of the diagonal "d" is:
d ≈ 5.657 inches
Therefore, the approximate length of the diagonal "d" of the cube is approximately 5.657 inches.
To find the length of the diagonal "d" of a cube, you 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, we can consider one face of the cube as the base of the right-angled triangle, with the diagonal "d" being the hypotenuse. The two sides of the right-angled triangle will be the edges of the cube.
Using the Pythagorean theorem, we have:
d^2 = e^2 + e^2
Where "d" is the length of the diagonal and "e" is the length of the edge.
Substituting the values, we get:
d^2 = 4^2 + 4^2
d^2 = 16 + 16
d^2 = 32
Taking the square root of both sides to find "d", we have:
d = √32
Approximating the square root of 32, we get:
d ≈ 5.657
Therefore, the approximate length of the diagonal "d" of the cube is approximately 5.657 inches.