Math, asked by kuchnhihy789, 2 months ago

Cube and Cuboid Formulas
total Surface Area = 6(side)2Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)Lateral Surface Area = 4 (Side)2Lateral Surface area = 2 height(length + breadth)Volume of cube = (Side)3Volume of the cuboid = (length × breadth × height)

Answers

Answered by Anonymous

Answer:

Definition of Cube and Cuboid

Cube: A cube is a three-dimensional shape which is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.

Cuboid: A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

Difference Between Cube and Cuboid

The sides of the cube are equal but for cuboid they are different.

The sides of the cube are square in shape but for cuboid, they are in a rectangular shape.

All the diagonals of the cube are equal but a cuboid has equal diagonals for only parallel sides.

Learn more differences between cube and cuboid here.

Shape of Cube and Cuboid

As we already know both cube and cuboid are in 3D shape, whose axes goes along the x-axis, y-axis and z-axis plane. Now let us learn in detail.

A cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions.

Properties of a Cuboid

Below are the properties of cuboid, its faces, base and lateral faces, edges and vertices.

Faces of Cuboid

A Cuboid is made up of six rectangles, each of the rectangles is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6 faces of cuboid.

The top face ABCD and bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and DAEH, CBFG are pairs of opposite faces. Any two faces other than the opposite faces are called adjacent faces.

Consider a face ABCD, the adjacent face to this are ABFE, BCGF, CDHG, and ADHE.

Base and lateral faces

Any face of a cuboid may be called the base of the cuboid. The four faces which are adjacent to the base are called the lateral faces of the cuboid. Usually, the surface on which a solid rests on is known to be the base of the solid.

In Figure (1) above, EFGH represents the base of a cuboid.

Edges

The edge of the cuboid is a line segment between any two adjacent vertices.

There are 12 edges, they are AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF and CD and the opposite sides of a rectangle are equal.

Hence, AB=CD=GH=EF, AE=DH=BF=CG and EH=FG=AD=BC.

Vertices of Cuboid

The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid.

A cuboid has 8 vertices A, B, C, D, E, F, G and H represents vertices of the cuboid in fig 1.

By observation, the twelve edges of a cuboid can be grouped into three groups, such that all edges in one group are equal in length, so there are three distinct groups and the groups are named as length, breadth and height.

A solid having its length, breadth, height all to be equal in measurement is called a cube. A cube is a solid bounded by six square plane regions, where the side of the cube is called edge.

Properties of Cube

A cube has six faces and twelve edges of equal length.

It has square-shaped faces.

The angles of the cube in the plane are at a right angle.

Each face of the cube meets four other faces.

Each vertex of the cube meets three faces and three edges.

Opposite edges of the cube are parallel to each other.

Cube and Cuboid Formulas

The formulas for cube and cuboid are defined based on their surface areas, lateral surface areas and volume.

Cube Cuboid

Total Surface Area = 6(side)2 Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

Lateral Surface Area = 4 (Side)2 Lateral Surface area = 2 height(length + breadth)