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DH
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Can some one tell me what are the diagonals of a cube?
Picture is better
Picture is better
Body diagonals of a cube are the line segments that connect opposite corners of a cube, passing through the center of the cube. They form the longest possible diagonal of the cube.
A cube has 4 body diagonals. Each diagonal connects 2 opposite corners of the cube, for a total of 8 corners. However, each diagonal is counted twice since it connects 2 corners, resulting in 4 unique body diagonals.
The length of a body diagonal in a cube can be calculated using the formula √3a, where a is the length of one side of the cube. This is derived from the Pythagorean theorem, where the length of the diagonal is the square root of the sum of the squares of the three sides.
The body diagonal is the longest possible diagonal that can be formed in a cube. It is also perpendicular to all edges of the cube and bisects them at the midpoint.
Body diagonals are important in various mathematical and scientific applications. In geometry, they help in understanding the properties of 3D shapes and calculating their surface area and volume. In physics, they are used in calculating the distance traveled by an object in motion and the direction of forces acting on an object. In engineering, body diagonals are important in structural design and analysis.