Need of Studying Surface Areas and Volumes
Surface areas and volumes play a significant role, in our day-to-day life. Look at your phone, it’s a cuboid, with blunt edges. Look at your room, it may be a cube or a cuboid, an oil-carrying tank is the combination of 2 hemispheres and a cylinder, a birthday cap it’s a cone, an aluminium bucket it’s a frustum, etc. So, unknowingly we have been surrounded, by many solids, which are combinations of some simple solids. Hence, this chapter will help us know how to calculate the surface area and volumes of the combination of figures.
Before moving toward the solids, we need to revise some of the terminologies which have already been discussed in the 9th class.
Lateral Surface Area
Lateral surface area is the area of a solid, in which the area of the top, and the area of the base are excluded. It is for solids like cubes, and cuboids, which have no curved surfaces. For example, a cube has a total surface area of 6πr2, and a lateral surface area is 4πr2 because the upper and the lower sides of the cube are excluded.
Curved Surface Area
Curved surface area is the area of a solid, in which the area of the top, and the area of the base are excluded. It is for solids like cylinders, cones, etc. For example, the total surface area of a cylinder is 2πr2 + 2πrh, and the curved surface area is 2πrh because the top and the bottom circular area have been excluded.
Note: The curved surface area of the solid changes, if the shape of the solid changes.
Total Surface Area
Total surface area is the total outer area, a solid occupies. For example, the total surface area of the cone is equal to the curved surface area of the cone and the area of the circular base i.e. πrl + πr2.
Note: The total surface area of the solid changes, if the shape of the solid changes.
Volume
Volume is the space occupied by a solid. For example, the volume of the cube is a3, the volume of the cylinder is πr2h, etc.
Note: Volume of the solid do not change, on changing the shape of the solid.
Also, Read
Surface Areas and Volumes Class 10 Maths Notes Chapter 13
CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes are an excellent resource, for knowing all the concepts of a particular chapter in a crisp, and friendly manner. Our articles, help students learn in their language, with proper images, and solved examples for better understanding the concepts.
Chapter 13 of the NCERT Class 10 Maths textbook delves into the world of Surface area and volume and covers various topics such as understanding the CSA, TSA of combined solids, volume of combined solids, converting from one solid to another solid, and the volume of the frustum. Notes are designed to give students a comprehensive summary of the entire chapter and include all the essential topics, formulae, and concepts needed to succeed in their exams.