The length of the edge of the cube, a%0D%0A%0D%0A , is 8 in. Find the length of the diagonal of the cube, d%0D%0A%0D%0A . Round the answer to the nearest tenth.
To find the length of the diagonal of the cube, we can use the Pythagorean theorem.
In a cube, each face is a square, and the diagonal of a square can be found using the Pythagorean theorem.
Let's call the length of the diagonal of the square face "s". We can find "s" by multiplying the length of one side of the square face by √2.
s = 8 * √2
s ≈ 11.3 in.
Now, since the diagonal of the cube passes through two opposite corners, we can use the Pythagorean theorem again to find the length of the diagonal of the cube.
Let's call the length of the diagonal of the cube "d". We have:
d² = 8² + 11.3²
d² = 64 + 127.69
d² ≈ 191.69
Taking the square root of both sides, we get:
d ≈ √191.69
d ≈ 13.8 in.
Therefore, the length of the diagonal of the cube is approximately 13.8 inches.