Cuboid | Formulas | Properties of Cuboid

A cuboid is a solid three-dimensional figure, which has 6 square faces or sides. Here we discuss here its definition, properties. Also, learn the surface area and volume formula for the Cuboid. In real-life match-box is a good example of the Cuboid.

What is Cuboid?

A cuboid is a three-dimensional shape has six, rectangle-shaped sides. Cuboid also have eight vertices (corners) and twelve edges. The angles in a cuboid are all right angles.

Cuboid

Part of Cuboid

Face:

A Cuboid is made up of six rectangles, each of the rectangle is called the face or sides. All four interior angles are right angles. In the given figure, the 6 faces of the cuboid are:
ABCD, EFGH, ADHE, BCGF, ABFE and DCGH.

Edge:

The edge of the cuboid is a line segment between any two adjacent vertices. A cuboid has 12 edges. Because all faces are squares and congruent to each other. In the given figure, the 12 edges of the cuboid are:
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG.

Vertex:

A point formed where three edges meet is called vertex. A vertex is a corner. A cuboid has 8 vertices. In the given figure, the 8 vertices of the cuboid are:
A, B, C, D, E, F, G, H.

Face Diagonals:

Face diagonals are line segments linking the opposite corners of a face. Each face has two, for a total of 12 in the cuboid. The length of the face diagonals is given by the formula

Length of Diagonal of Face of the Cuboid = √(length2 + breadth2 )

Space Diagonals:

Space diagonals are line segments linking the opposite corners of a cuboid, cutting through its interior. A cuboid has 4 space diagonals. The length of the space diagonal is given by the formula

Length of Diagonal of Cuboid = √(length2 + breadth2 + height2)

Perimeter

The perimeter of a cuboid found by adding all the sides.

Perimeter = 4(length + breadth + height)

Volume:

The volume of the cuboid is equal to the product of the area of one surface and height. Volume is measured in cubes (or cubic units)

Volume = length × breadth × height

Surface Area:

Sum of the areas of all its 6 rectangular faces

Surface Area = 2(lb + bh +lh)

Where, l is lenght, b is breadth, h is height

Lateral surface

The sum of surface areas of all sides except the top and bottom face of solid is defined as the lateral surface area of a solid.

Lateral surface = 2h(l +b)

Properties of Cuboid

• It has 12 edges
• It has 8 corners or vertices
• It has 6 faces.
• All faces of the cuboid are in a rectangle shape.
• The angles in a cuboid are all right angles
• The edges opposite to each other are parallel.

I hope, this article will help you a lot to understand the Cuboid | Formulas | Properties of Cuboid. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

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