The length of the edge of the cube, a
, is 8 in. Find the length of the diagonal of the cube, d
. Round the answer to the nearest tenth.
(1 point)
The diagonal of a cube can be found using the Pythagorean theorem. Since a cube has all sides equal, the diagonal is the hypotenuse of a right triangle with sides equal to the length of the edge.
Using the Pythagorean theorem:
d^2 = a^2 + a^2 + a^2
d^2 = 3a^2
Taking the square root of both sides:
d = √(3a^2)
Substituting in the given value of a = 8 in:
d = √(3(8^2))
d = √(3(64))
d = √(192)
d ≈ 13.9 in
So, the length of the diagonal of the cube is approximately 13.9 in.