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A Complete Guide On Surface Areas And Volumes
As a student of standard 9, you are already introduced with various geometrical shapes and sizes. Starting from simple two-dimensional shapes like triangle, quadrilaterals, etc., now you are learning about complex three-dimensional shapes such as cone, cube, cylinder, etc.
Initially, you may face little difficulty to understand these shapes and their measurements. However, a thorough understanding of the surface area and volume formula of these shapes can clear all your doubts and concepts.
Hence, a systematic explanation of geometrical formulas can help you understand the chapter of surface area and volume class 9. Once you adopt all the formulas and theorems of this chapter, it will be easy for you to solve problems from both 9th and 10th standards.
Thus, let’s start learning!
Volume And Surface Area Of Solids
In this class 9 surface area and volume, you will learn about four shapes. Here are the formulas of volume and surface area of cone, cube, sphere, and cylinder-
Cone
This is a 3D geometric shape created by two lines segments connecting a common point. This point is known as vertex or apex. This shape tapers from a smooth and flat base to the apex. Following is the diagram of a cone.
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Here are the formulas of volume and surface area of cone-
If the vertical height of the cone = h
Radius of the base = r
Slant height = l
Then, volume = 1/3 π r2 h
Total surface area = πr2 + πrl
Lateral area = πrl
Sphere
It is a geometrical shape in 3D space that is similar to the outer surface of a planet or ball. Mathematically, it can be defined as a set of points that are situated at an equal distance from any given point. You can check the below diagram of a sphere for reference.
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To solve mathematical problems related to the sphere, you need to understand the formulas of surface area and volume of spheres.
If the radius = r,
Then, volume = 4/3 πr3
Surface area = 4πr2
Cylinder
This is a solid curvilinear shape with the surface formed by equal and fixed-distant points from a given line. For example, you can imagine the cooking gas cylinder and also find the diagram below. The diagram will help you to understand the cylinder area and volume formulas.
(Image to be added soon)
Now, the formula of volume and surface area of cylinder-
If the radius of a cylinder = r
Height = h
The lateral surface area without the top and bottom surface = 2πrh
The total surface area including top and bottom surface = 2πr (r + h)
Volume = πr2h
Cube and Cuboid
A cube is formed with six square faces or sides, and each vertex is the meeting point of three sides. However, a cuboid also has six faces, but the cuboid faces can be any quadrilateral. Mostly, cuboid faces are rectangular.
First, see the diagram of a cube.
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Now, check the cuboid diagram to understand the difference between these two shapes.
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Following are the formulas of volume and surface area of a cube –
If the length of one side of a cube = a,
Then, surface area = 6a2
Volume = x3
Now, let’s move to the surface area and volume formula of a cuboid-
If the height of a cuboid = h
Length = l
Width = w
Then, surface area = 2 (hl + lw + wh)
Volume = hlw
With the help of these above formulas, you can easily solve volume and surface area problems of cone, cube, cuboid, sphere, cylinder.
However, if you require any more details on surface areas and volumes formula, you can check our Vedantu website. Also, you can ask your doubts out by attending our online classes where experts will help you with your problems.
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