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JEE Exam » JEE Study Material » Mathematics » Solids

Solids

In this article, we will learn about the solids, their properties, attributes, and various types of solid shapes.

Table of Content
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Solids or three-dimensional shapes are three-dimensional shapes with three (or more) dimensions in Geometry. Solid geometry is the study of the characteristics, volume, and surface area of three-dimensional shapes. Geometry is primarily concerned with two sorts of shapes: flat and solid. 

Solids

Three-dimensional shapes, often known as solids, are shapes that occupy space. Figures with three dimensions – length, breadth, and height – are also known as solid shapes. A sphere, or three-dimensional form, is a ball, whereas a circle drawn on a piece of paper is a two-dimensional figure. Similarly, solid shapes such as a table, chair, notebook, pen, and so on are all around us. 

Some of the attributes of solid geometric shapes

  1. Faces: The faces of solid figures are the single flat figures that make up the solid figures. It could be square, rectangular, or any other polygon. 

  2. Edges: The edges of solid objects are the line segments between two faces where the two faces meet. 

  3. Vertices: Vertices are the intersection points where the edges of solid figures meet. Three faces meet at a single vertex in most cases. Vertices are the plural version of a vertex. 

Types of solid shapes

The many forms of solids can be considered as three-dimensional extensions of various two-dimensional shapes, such as a cube being a three-dimensional extension of a square. A cylinder can also be thought of as a three-dimensional extension of a circle. This method of solid analysis will make it easier to understand the equations and properties of various materials. 

Cube

A cube is a two-dimensional solid with six square faces. It can be thought of as a three-dimensional expansion of the square. The following are its characteristics: 

  1. It has the same edges and faces on all sides. 

  2. A total of eight vertices. 

  3. There are 12 edges in all. 

  4. 6 different faces.

  5. All of the angles are 90° degrees. 

Cuboid

A cuboid, also known as a rectangular prism, is a solid form of two-dimensional rectangular sides. It possesses the following characteristics: 

  1. Faces and edges on opposite sides are equal. 

  2. A total of eight vertices. 

  3. There are 12 edges in all. 

  4. 6 different faces. 

  5. All of the angles are 90° degrees. 

Prism

A prism is solid with a base and top that are identical polygons and lateral sides that are parallelograms. Triangular prisms, square prisms, and pentagonal prisms are among the examples. The following are some of the properties of a triangular prism: 

  1. There are six vertices.

  2. 9 edgings.

  3. Two triangles and three rectangles make up the five faces. 

Pyramid

A pyramid is a solid having a base that is any polygon and side faces that are triangles with a shared vertex. The square pyramid, for example, has a square base and four triangular side faces. The following are some of the characteristics of a square pyramid: 

  1. There are 5 vertices. 

  2. 8 edgings. 

  3. There are five faces. 

Cylinder

A cylinder is a solid shape with two round bases and a curving surface. A cylinder has the following properties: 

  1. No vertices. 

  2. Two edges. 

  3. Two flat faces, both of which are circles, and one curving surface. 

Cone

A cone is a solid object having one circular base attached to a curved surface and a single vertex. The following are some of the most important characteristics of a cone: 

  1. A single vertex 

  2. 1 slant 

  3. 1 circle with a single flat face only one curved face 

Sphere

A sphere is a solid that is perfectly spherical in shape. The following are some of the sphere’s most important characteristics: 

  1. It does not have a vertex. 

  2. It doesn’t have any edges. 

  3. It doesn’t have any level surfaces. 

  4. It just has one curved face. 

Conclusion

Solids, often known as three-dimensional things, have three dimensions: length, width, and height. Faces, edges, and vertices define solid forms. Learning about solid shapes will benefit us in our daily lives because they are central to and reliant on most of our actions. 

faq

Frequently asked questions

Get answers to the most common queries related to the JEE Examination Preparation.

How many solid shapes are in mathematics?

Ans. Cubes, cuboids, prisms, pyramids, platonic solids, torus, cones, cylinders, and spheres are the most common sol...Read full

What is a solid shape?

Ans. Solid shapes are three-dimensional shapes with three dimensions: length, breadth, and height. &nb...Read full

What is the difference between a cube and a cuboid?

Ans. A cube has six identical square-shaped faces, but a cuboid has rectangular faces. The cube and the cuboid have ...Read full

What are the properties of solid shapes?

Ans. Three-dimensional things are solid shapes. They come in three sizes: long, wide, and tall. They take up space i...Read full

What are the flat and solid shapes?

Ans. Flat shapes, also known as plane shapes, are two-dimensional objects made up of straight, curved, or both lines...Read full

Ans. Cubes, cuboids, prisms, pyramids, platonic solids, torus, cones, cylinders, and spheres are the most common solid shapes.

 

Ans. Solid shapes are three-dimensional shapes with three dimensions: length, breadth, and height.

 

Ans. A cube has six identical square-shaped faces, but a cuboid has rectangular faces. The cube and the cuboid have similar structures, although there are some variances in edge length, diagonals, and faces.

 

 

 

Ans. Three-dimensional things are solid shapes. They come in three sizes: long, wide, and tall. They take up space in the universe because they are three-dimensional. Edges, vertices, faces, and other features are used to identify solid shapes.

Ans. Flat shapes, also known as plane shapes, are two-dimensional objects made up of straight, curved, or both lines. Solid shapes, on the other hand, are three-dimensional shapes with length, width, and height. The dimensions are the difference between flat and solid shapes. A square, for example, is a flat shape, but a cube, which is a 3D shape, is its counter solid.

 

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