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.
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.
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.
Surface Area: 6L2 where L is the dimension of its side.
Volume: L3 where L is the dimension of its side.
Surface Area: 2(LB+ BH+ LH).
Lateral Surface Area: 2(L + B) H [where L= Length, B= Breadth and H= Height]
Right Circular Cylinder
Lateral Surface Area: 2πRH.
Total Surface Area: 2πR (H + R)
Volume: πR2H [where R= Radius, H= Height].
Right Circular Cone
Lateral Surface Area: πRL
Total Surface Area: pπR (L + R)
Volume: ⅔ πR2H [where R= Radius, L=Slant Height and H= Height]
Surface Area: 4πR2
Volume: 4/3 πR3 [where R= Radius]
Curved Surface Area: 2πR2
Total Surface Area: 3πR2
Volume: ⅔ πR3 [where R= Radius].
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Q1. How are the Surface Area and Volume of a Cone Determined?
Ans. Since the cone is a three-dimensional shape, it can easily be imitated in any real-life object, such as a conical flask. The cone has one apex and it shares one common point with all of its line segments. Since the base of the cone is more or less like a circle, it doesn’t have an apex and the apex of the cone passes through the centre of the circular base. Therefore, the surface area of the cone whether lateral or total is determined by the radius of the circular base and by its slant height. Similarly, the volume is determined by its radius, slant height and height.
Q2. How are the Surface Area and Volume of a Right Circular Cylinder Determined?
Ans. A cylinder is a basic geometric shape. It is usually obtained through curving a rectangle and is, therefore, highly imitable in real-life objects such as cylindrical pipes, jars, etc. Since the base of a right circular cylinder is a circle, its centre coincides with both the circular faces of the cylinder. Therefore, through this centre, the height of the cylinder passes and is determined. Therefore, the lateral, as well as the total surface area of a right circular cylinder, is determined by its height and radius. Similarly, the volume of the right circular cylinder is also determined by the two.