Cuboid

A cuboid is one of the most important geometrical shapes and it has three dimensions. The geometrical formulas regarding cuboid, like the volume of a cuboid, the surface area of a cuboid, the perimeter of a cuboid, the face diagonal of a cuboid, the space diagonal of a cuboid, and the discussion around the cuboid shape are common topics for the competitive exams. The article discusses all the properties of a cuboid. The properties make the cuboid an interesting aid for scientific experiments and research besides also showing their utility in the daily courses of life here.

Difference between cube and cuboid

A cube has equal surfaces and surface areas. The cuboid has equal size squares in all its spaces. The cuboid has rectangular surface areas and they are not equal, only the ones facing each other are equal in size.

Definition of cuboid

A cuboid is also known as a polyhedron. It also has the dimensions of a cube, it has 6 faces and those are also considered surfaces. The vertices are 8 in number. There are 12 edges in a cuboid. The usual cuboid is rectangular in two faces and has nothing but right angles. The cuboid looks somewhat like a cube. The cuboid has a base and 4 adjacent faces. When a face is considered the base of the cuboid, then the faces which touch it with the help of the edges are known as lateral faces. The cuboid is used for calculations of geometry, trigonometry, and mensuration.

A rectangular cuboid has equal sizes for all the opposite faces. The square cuboid has at least two square faces.

Formulas for cuboid

The formula for the usual polyhedron is F + V = E + 2.

Here F is used for the face of the structure, V is used for the vertices of the structure, E is used for the edges of the structure. The faces are the surfaces, the edges are the places where two surfaces join together and the vertices are the intersections of three faces of the cuboids. The edges work as segmenting lines between two adjacent faces.

The volume of a cuboid

When the dimensions of a rectangular cuboid are x, y, and z, then the volume of the cuboid is XYZ. The volume is calculated by multiplying the dimensions.

The surface area of a cuboid

When the dimensions of a rectangular cuboid are x, y, and z, then the total surface area of the cuboid is 2 ( xy + yz + xz ). The total surface area is calculated by multiplying every two components, adding three multiplications, and then multiplying the entire number with 2.

The diagonal length of a cuboid

When the dimensions of a rectangular cuboid are x, y, and z, then the diagonal length is calculated by the square root of the addition of all the squares of the dimensions. So, the formula will be

ü ( x² + y² + z² ).

Face diagonal of a cuboid

When the dimensions of a rectangular cuboid are x, y, and z, then the face diagonal is calculated by adding the square of the length with the square of the breadth of the cuboid and then working out its square root. So, if x is considered the length and y is considered the breadth, the formula is

ü ( x² + y²).

Space diagonal of a cuboid

When the dimensions of a rectangular cuboid are x, y, and z, then the space diagonal is calculated by adding the square of the length with the square of the breadth and then the square of the height of the cuboid and then working out its square root. So, if x is considered the length, y is considered the breadth, and z is considered the height of the cuboid, the formula is

ü ( x² + y² + z² ).

The perimeter of a cuboid

When the dimensions of a rectangular cuboid are x, y, and z, then the space diagonal is calculated by adding the length, breadth, and height of the cuboid together and then multiplying the result with 4. So, if x is considered the length, y is considered the breadth, and z is considered the height of the cuboid, then the formula will be 4 ( x + y + z )

Conclusion

This article has discussed the geometrical formulas regarding cuboids, like the volume of a cuboid, the surface area of a cuboid, the perimeter of a cuboid, the face diagonal of a cuboid, the space diagonal of a cuboid, and the discussion around the cuboid shape. It is necessary to have sufficient knowledge about the cuboid shape along with other geometrical structures with three dimensions like a cube, cone, cylinder, etc.