Common Solid Figures

In third grade geometry we will discuss in brief about some of the common solid figures named below:
(i) Cube: Definition of cube, parts of a cube, properties of a cube.

(ii) Cuboid: Definition of cuboid

(iii) Cylinder: Definition of cylinder

(iv) Cone: Definition of cone

(v) Sphere: Definition of sphere

Definition of a cube:

An object which looks like solid box-shaped that has six identical square faces.

A cube has 6 equal and plane surfaces. All the faces of a cube are square in shape.

In a cube there are 6 plane surfaces. There are 8 vertices and 12 edges.

Parts of a Cube

Two adjoining plane – surfaces meet at an edge. There are 12 edges in a cube and all the 12 edges are equal in length. These edges are straight edges.

The meeting point of two edges is called a vertex. In a cube there are 8 such vertices.

Parts of a cube:

(i) Face: Face is also known as sides. A cube has six faces and all the faces of a cube are square in shapes. Each face has four equal sides.

(ii) Edge: When two edges meet each other a line segment formed. There are 12 edges in a cube. All the 12 edges are equal in length because all faces are squares. These edges are straight edges.

(iii) Vertex: When three edges meet each other a point formed. There are 8 vertices in a cube.

(iv) Face Diagonals: Face Diagonals of a cube is the line segment that joins the opposite vertices of a face. There are 2 diagonals in each face so altogether there are 12 diagonals in the cube.

(v) Space Diagonals: Space diagonals of a cube are the line segment that joins the opposite vertices of a cube, cutting through its interior. There are 4 space diagonals in a cube.

Properties of a cube:

Volume: The volume of a cube is s3 where s is the length of one edge.

Surface Area: The surface area of a cube is 6s2, where s is the length of one edge.


Definition of cuboid:

The cuboid has 6 rectangular faces. The opposite rectangular plane surfaces are identical (equal in all respects). It has 8 vertices and 12 edges.

In a cuboid there are 6 rectangular plane surfaces. There are 8 vertices and 12 edges.

Parts of a Cuboid

A cube is also a cuboid having all its 6 faces equal and square. Thus, a cube has all the six faces identical, whereas a cuboid has the opposite faces identical.

Properties of a cuboid:

Formulas for the above rectangular box:

Volume: The volume of a cuboid is lwh, where l is the length, w is the width and h is the height.

Lateral Surface Area: The lateral surface area of a cuboid is 2lh + 2wh, where l is the length, w is the width and h is the height.

Surface Area: The surface area of a cuboid is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.


Definition of cylinder:

A cylinder stands on a circular plane surface having circular plane surfaces on its top and bottom. Thus a cylinder has two circular plane surfaces, one at its base and another at its top. It has a curved surface in the middle.

It has two edges, at which the two plane surfaces meet with the curved surface. These edges are curved edges.

In a cylinder there are 2 plane surfaces and 1 curved surface. There are 2 edges and no vertices.

Parts of a Cylinder

The base and top of a cylinder are of the same shape (circular) and size. Thus, both are identical.


Definition of cone:

A cone has one plane circular surface, i.e. its base and only one curved surface. In a cone there is 1 plane surface and 1 curved surface. There are 1 edge and 1 vertex.

Parts of a Cone

It has one edge which is formed by the circular plane surface meeting with the curved surface. The edge of a cone is a curved edge.


Definition of sphere:

The ball-like shape is called a sphere. In sphere there is curve surface, no edge and no vertex.

Parts of a Sphere

Some of the common solid figures are explained above in brief with the labeled diagram to get the basic ideas of the solid shapes.


Note:

(i) The surface of solid is called face.

(ii) Edge is formed when two faces meet.

(iii) The point where 3 faces meet is called the corner.

Related Concepts

Basic Shapes

Surfaces of the Solids

Common Solid Figures

Points, Lines and Shapes

Line-Segment, Ray and Line

Types of Lines

Geometrical Design and Models


3rd Grade Math Lessons

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