Surface Area and Volume Formulas Class 9 - An Introduction
When it comes to studying Mathematics, the branch of Mensuration is considered to be one of the most practical branches. This is because Mensuration is the branch of Mathematics in which plane and solid figures like a cube, cuboid, sphere, cone, pyramid, etc. are studied with regards to their surface area and volume. For calculating this, there are specific formulas to be followed. Therefore, here in the Chapter Surface Area and Volume Class 9 by Vedantu, all formulas of the plane (2D) and solid (3D) figures shall be discussed.
The students who have Math as a subject have to keep up with certain topics of importance such as the Surface Areas and Volumes. It can be said that there are a few of the topics that are of utmost importance. The reason is mostly due to the fact that these concepts come in handy to the students at the time of their higher education. The topics such as these are ones which the students can find the most interesting as well. It is important for any class 9 student to have a good understanding of some of the most basic concepts that there are. This will definitely come in aid for them while they have to appear for their Math exams and score well in them.
There are a few of the topics that come in handy while getting prepared for your exams. When it comes to the topics such as the surface areas and volumes, one can get all the formulas. It is important that the students get to understand the formulas and learn them as well. There are specific formulas that the students learn so that they can apply them as per their knowledge.
All Formulas of Surface Area and Volume Class 9 - The Figures
As stated earlier, the field of Mensuration is concerned primarily with the study of solid and plane figures. These figures are three-dimensional in nature and are observed in nature. For example, if one were to understand and calculate the surface area of a Rubik’s cube, they would look at the formulated way of obtaining its surface area and then can successfully understand its surface area. Thus, through these Surface Area and Volume Class 9 Formulas, some of those figures shall be learned about with regards to their surface area and volume.
Since this field of study is concerned with the figures and their dimensional calculations, the formulas of Surface Area and Volume Class 9 are the ideal formulas for three-dimensional study. So, the formulas that are proposed through the study of mensuration are referred to understanding the ideal figures and their dimensions. However, since no real object imitating a pyramid is ever ideal or perfect, these Class 9 Surface Area and Volume Formulas do not obtain the absolute dimensional answers to real-life objects that imitate a plane or solid figure.
The Formula of Surface Area and Volume Class 9 - A Brief Analysis of the Figures
All the formulas of Surface Area and Volume Class 9 have been derived and deduced through a thorough understanding of the various contributing elements of the figures such as its length, breadth, height, circumference, etc. This Class 9 Surface Area and Volume Formula set have therefore been provided with regards to the figures of the cube, cuboid, right circular cylinder, right circular cone, sphere, and hemisphere. Therefore, these are the figures that the Surface Area and Volume Formulas Class 9 deals with.
Class 9 Maths Surface Area and Volume All Formulas - The Complete List
Cube
Surface Area: 6L2 where L is the dimension of its side.
Volume: L3 where L is the dimension of its side.
Cuboid
Surface Area: 2(LB+ BH+ LH).
Lateral Surface Area: 2(L + B) H (where L= Length, B= Breadth and H= Height)
Volume: LBH
Right Circular Cylinder
Lateral Surface Area: 2 \[ \pi RH \].
Total Surface Area: \[2\pi R(H + R)\]
Volume: \[\pi R^{2}H\] (where R= Radius, H= Height).
Right Circular Cone
Lateral Surface Area: \[ \pi RL \]
Total Surface Area: \[\rho \pi R(L + R)\]
Volume: \[\frac{2}{3}\pi R^{2}H\] (where R= Radius, L=Slant Height and H= Height)
Sphere
Surface Area: \[4\pi R^{2}\]
Volume: \[\frac{4}{3}\pi R^{3}\](where R= Radius)
Hemisphere
Curved Surface Area: \[2\pi R^{2}\]
Total Surface Area: \[3\pi R^{2}\]
Volume: \[\frac{2}{3}\pi R^{3}\] (where R= Radius).
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FAQs on CBSE Class 9 Maths Surface Areas and Volumes Formulas
1. How are the Surface Area and Volume of a Cone Determined?
A cone is a three-dimensional figure. So, it is very easy to perceive it as a real-life object. One can take the example of a conical flask. The figure is one that only has one apex, and there are all line segments that the apex is the one common point for. One must know that the base of the cone is actually a circle. Though this circle does not have a center point, it does have the apex of the cone perpendicular to it right in the middle. Therefore, we can conclude that the surface area of a cone can be determined by its slant height, the radius of the circle, and the distance of the apex to the base of the cone. These are also the same factors that can determine the volume of a cone.
2. How are the surface area and volume of a right circular cylinder determined?
A right circular cylinder is one of the basic geometrical shapes. You can think of it as a rectangular paper that can be curved into a cylinder. You can notice various real-life objects such as jars, cylindrical pipes, etc. You can easily find that the right circular cylinder has its axis perpendicular to its base, which is a circle. Therefore, the surface area, as well as the volume of the cylinder, can be determined with the help of the height as well as the radius of the cylinder.
3. What is the best way to prepare the volume of a figure for class 9 students?
The volume of a figure can be described as how much of a liquid you can fill in it, for example. This can let you know of the space that is present in a figure such as a cube, cone, sphere, etc. There are specific formulas to take out all the volume of any given figure. To apply these formulas, especially at the time of exams, the students are supposed to learn them thoroughly. That, they can do with the help of Vedantu and the detailed insights it offers.
4. How can a student get a good understanding of the surface area of any figure?
The surface area is basically the area of all the faces of a figure that are outside. Think of it as wrapping paper that you need to wrap the said figure in. For taking out the surface area of a given figure, it is significant for one to be acquainted with the formulas and to fulfill the requirements of specifications in those formulas. A student can have a good understanding of the formulas with Vedantu's expert teachers and the study material that is of significance for Class 9 students of Math.
5. Are there any online study materials to help the students prepare better for their exams?
Yes, there are study materials online that the students can take the help of at any point of their preparations. The best platform for doing this is Vedantu, where they can find not only the formulas but also their applications. They can also rest assured to find the applications pretty descriptive, which makes it easier for them to understand all of the steps. The students can also get much of their preparations done with the help of such online study material for Maths Class 9.