Essential Surface Area & Volume Formulas for Quick Revision
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 Surface Areas and Volumes Formulas for CBSE Class 9 Maths
1. What are the formulas of surface area and volume for class 9?
In Class 9 maths, surface area formulas include:
- Cube: $6a^2$
- Cuboid: $2(lb + bh + hl)$
- Cylinder: $2\pi rh + 2\pi r^2$
- Cube: $a^3$
- Cuboid: $lbh$
- Cylinder: $\pi r^2 h$
2. What are the formulas for class 9 maths?
The main formulas for Class 9 maths include concepts from algebra, geometry, and mensuration. Key ones are:
- Area of triangle: $\frac{1}{2} \times base \times height$
- Pythagoras theorem: $a^2 + b^2 = c^2$
- Volume of cube: $a^3$
3. What is the formula of volume in maths class 9?
In Class 9 maths, the volume formula depends on the shape. For a cube, it is $a^3$, for cuboid, $l \times b \times h$, and for a cylinder, $\pi r^2 h$. Volume measures the amount of space inside a 3D solid.
4. What is the TSA formula for Class 9?
The Total Surface Area (TSA) formula in class 9 depends on the solid's type. Examples include:
- Cube: $6a^2$
- Cuboid: $2(lb + bh + hl)$
- Cylinder: $2\pi r(h + r)$
5. What is lateral surface area in class 9 surface areas and volumes?
In Class 9 surface areas and volumes, lateral surface area (LSA) is the area of sides, excluding bases. For example:
- Cuboid: $2h(l+b)$
- Cylinder: $2\pi rh$
6. How do you find the curved surface area of a cylinder in class 9?
The curved surface area (CSA) of a cylinder in class 9 is $2\pi rh$, where $r$ is the radius and $h$ is the height. It calculates only the side curved part, not the circles at the ends, of the cylinder in mensuration problems.
7. Why are surface area and volume formulas important in class 9 maths?
Surface area and volume formulas are important in class 9 maths because they help solve real-life problems like:
- Finding material needed to cover objects
- Calculating storage space
- Understanding geometric properties
8. What is the formula for the volume of a cone for class 9 students?
For class 9 students, the volume of a cone is given by $\frac{1}{3}\pi r^2 h$, where $r$ is the radius and $h$ is the height. This formula calculates the space inside the cone and is essential in mensuration problems.
9. How can you find the total surface area of a cuboid in class 9 maths?
To find the total surface area (TSA) of a cuboid in class 9, use the formula $2(lb + bh + hl)$, where $l$ is length, $b$ is breadth, and $h$ is height. This formula adds all six faces’ areas for complete coverage.
10. What are the key formulas for surface areas and volumes of a sphere in class 9?
In class 9 maths, key formulas for a sphere are:
- Surface area: $4\pi r^2$
- Volume: $\frac{4}{3}\pi r^3$
11. What is the formula for the volume of a cylinder in CBSE class 9?
In CBSE class 9 maths, the formula for the volume of a cylinder is $\pi r^2 h$. Here, $r$ is the radius of the base and $h$ is the height. This formula measures how much space is inside the cylinder.
