[Maths Class Notes] on Solids Pdf for Exam

This section will introduce the students to one of the most important aspects of Maths, i.e, Solids. Solids are very important from the perspective of Maths and measurement, and the analysis of their volume, surface area, and total area is very much useful in day-to-day life. In our day-to-day life, we come across a number of different types of solids. A room may be in the shape of a cube or cuboid, the cricket ball is in the shape of a sphere, the birthday hat or ice cream is in the shape of a cone, water tanks on the rooftops are in the shape of a cylinder, the gift boxes are in the shape of cubes or cuboids, etc. Similarly, different things that we use in our day-to-day life are in the shape of different solid figures, a combination of two or more solid figures of the same types or different types, or have a slightly modified shape than the actual solid. For example, a water bottle can be a combination of two different cylinders, one of larger radius and another of a smaller radius, a pen is a combination of two cylinders, a refill in the shape of a cylinder with a smaller radius and the body is also in the shape of a cylinder with a larger radius, a dome is formed by the combination of two types solid shape, i.e., a hemisphere and a cylinder/cone. The hemisphere is mounted on a cylinder, or it may be mounted on a cone.

The discussion will be on different types of solids, like a cylinder, prism, sphere, cube, rectangle, etc., volume, surface area, and total area of the solids, properties of the sides and diagonals of the solids, the characteristic of their interior and exterior angles, and so on. Students will also be introduced to a formula list that will summarise the formulae for volume and different types of areas of the respective solids.

The formula list provides a relationship between the different parameters of the solid figure and its three-dimensional aspects of volume and area. Using the list makes the memorization of the formulae for different types of solids very easy and helps in creating links between different formulae. Some solved examples are also provided for better understanding and comprehension of the students.

Geometry basically deals with two types of shapes: plane shapes and solid shapes. Let us study what solids are in maths. We have observed that a plain picture can be drawn on paper, it does not occupy any space. But if we keep a real picture on that piece of paper, it occupies some space, and such shapes are called solid shapes or solids or three-dimensional shapes.

Solid geometric shapes or three-dimensional geometry deals with solids or three-dimensional shapes. Solids examples are cubes, cuboids, spheres, cylinders, cones, etc. Let us study types of solid shapes and solid shapes properties.

What are Solids in Maths?

The shapes that occupy space are called three-dimensional shapes or solids. Solid shapes can also be defined as figures having three dimensions – length, width, and height. A ball is an example of a sphere, which is a three-dimensional figure, while a circle drawn on a piece of paper is a two-dimensional figure. Similarly, we have many solid shapes all around us, like a table, chair, notebook, pen, etc. Here are some of the solid examples and solid shapes properties.