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RD Sharma Class 9 Solutions Chapter 20 - Exercise 20.2

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Last updated date: 23rd May 2024
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RD Sharma Class 9 Solutions Chapter 20 - Surface Area and Volume of Right Circular Cone (Ex 20.2) Exercise 20.2 - Free PDF

You can download a free PDF of RD Sharma Class 9 Solutions Chapter 20 - Surface Area and Volume of Right Circular Cone Exercise 20.2 that is solved by subject-matter experts of Vedantu. The RD Sharma Class 9 Maths PDFs contain all the questions of Chapter 20 - Surface Area and Volume of Right Circular Cone with solutions to help students revise the complete syllabus and score more marks in the exams. They can also register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams on Vedantu. Furthermore, students can also register online for Class 9 Science tuition on Vedantu to score more marks in the exams. Vedantu is a leading learning platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths students who are looking for better solutions can download Class 9 Maths NCERT solutions to help them revise the complete syllabus and score more marks in the board examinations.

 

Having an axis perpendicular to the plane of the base is what defines a right circular cone. A cone is a 3D geometric figure with a circular top and a curved bottom. It is made up of a circular top and curved bottom that meet at a point toward the top of the figure. Cones have an apex and a base. The apex or vertex is located at the end of the cone and the base is located at its base. When a triangle is rotated, one of its two short sides becomes the rotation axis and forms a cone.

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What are Right Circular Cones?

Right circular cones means the cones with an axis perpendicular to the base plane. An often used geometric representation of right circular cones is the right triangle that revolves around one of its legs. In the figure below, we can also see that the right-angled triangle, when revolved, results in a cone. The base of a right circumcircle is the shape of the base of a right circular cone.

 

Cones with Right Circular Surface Areas

In 3-D space, a cone's surface area is defined as the total area covered by the surface of the 3-D shape. Using square units ( cm2, m2, ft2) it is expressed as cm2. To understand the surface area of a right circular cone, let's cut and open it up. Curved surfaces form sectors with radius 's', as shown below.

 

(Image will be uploaded soon)

 

A right circular cone can have two types of surface area:

  • CSA, or curving surface area

  • TSA, or total surface area

A right circular cone has a curved surface area

A right circular cone is said to have a curved surface area if it occupies the entire curved surface. When we refer to a right circular cone's curved surface area, we do not include the area at the base. A curved surface area is sometimes also called a lateral surface area.

 

Right Circular Cone Surface Area

The area of a right circular cone, including the base, is defined as the surface area of the cone. Next, we will review the formulas to determine both CSA and TSA of a right circular cone.

 

1. The formula for the surface area of a right circular cone

It has been shown in the previous section that a right circular cone can have two surfaces: curved surfaces and total surfaces. Different formulas can be used to calculate TSA and CSA for a right circular cone.

 

2. Surface area formula for curved surfaces

In order to calculate CSA for a right circular cone, use the following formula:

A cone's curved surface area = The region with a radius equal to the slant height, denoted by 's',

Curved surface area of a cone = πrs = πr√(r2 + h2)

Specifically,

  • The radius of the base is r

  • and h is the height of the right circular cone

  • where s is the slant height

 

3. The formula for computing total surface area

Using the following formula, the TSA formula for a right circular cone can be calculated,

The surface area of a cone is equal to the average of the area of the circular base and the surface area of the curved cone (sector area).

 

In the case of a cone, the total surface area is equal to πr2 + πrs

 

A cone's total surface area is equal to πr2 + πr√(r2 + h2)

Specifically,

  • r = Base radius

  • h = Height of right circular cone

  • s = Slant total included the height of right circular cone which is the total slant height

 

It is possible to refer to only the surface area of a right circular when discussing the total surface area. We always calculate the surface area whenever we are asked to do so, meaning we have to find the total area of the cone given.

 

Volume of a Right Circular Cone

Objects defined in 3-dimensional space are said to occupy a certain volume of the right circular cone. In3 is equal to in3(cube), m3(cube) is equal to m3(cube), cm3(cube) is equal to cm3. If a right circular cone has a circular base with radius 'r' and height 'h', it will have a volume that equals 1/3 of the product of that base's area and its height. Based on the radius and height of the base, the volume of the right circular cylinder can be calculated.

FAQs on RD Sharma Class 9 Solutions Chapter 20 - Exercise 20.2

1. How will RD Sharma Class 9 solutions for Chapter 20 - Surface Area and Volume of Right Circular Cone help with the exam preparation?

RD Sharma Class 9 Solutions Chapter 20 - Surface Area and Volume of Right Circular Cone  Can you help you in the following mentioned ways-

  1. Deep concept learning- By learning the topics and concepts deeply you get a fair bit of idea about the easy and tough concepts or topics and which topic needs more attention and practice.

  2. As per the exam point of view, you have to rest assured about the easiest way to get the solutions. by following this pattern you can have the solutions in a simple manner. 

You can avail all the well-researched and good quality chapters, sample papers, syllabus on various topics from the website of Vedantu and its mobile application available on the play store. 

2. Describe the significance of Class 9 Chapter 20- Surface Area and Volume of Right Circular Cone.

Chapter 20 - Surface Area And Volume of the Right Circular Cones has much significance. Listed below are a few:

  1. The Area and Volume of Right Circular Cones- For a right circular cone with radius 'r', height 'h', and slant height 'l', we have: Curved surface area of right circular cone = πrl. Right circular cones have a surface area of π(r + l) r. A right circular cone has a volume of 1/3πr2 h

  2. You can calculate the formula even with diagrams if you mark the ends of each cone and mention each side of it.

3. Following the concepts of RD Sharma Class 9 Chapter 20 Maths, solve the given question:


Assume a cone has a height and slant height of 21 cm and 28 cm respectively. Determine the volume.

The height of the cone i.e. the total height (h) = 21 cm

 

The slant height of the cone (l) is 28 cm

 

Calculate the radius of the cone:

 

We know that l2 = r2 + h2

 

282 = r2 + 212

 

or r = 7√7 cm

 

As a result,

 

We know that volume of a cone = 1/3 * r2h

 

= 1/3 x π x (7√7 )2 x 21

 

= 2401 π


Thus, the cone has a volume of 2401 π cm3.


4. Following the concepts of RD Sharma Class 9 Chapter 20 Maths, is the surface area of a right circle equal to its total surface area?

Total surface area is essentially the total area underneath a sphere is defined as the total area or region under the sphere, including the area under the circular base. The top and bottom of a cylinder are two congruent circles that are known as bases. The height of a cylinder is equal to the distance between its circular bases, while its radius equals the distance between its circular bases. e calculated using the formula, Total surface area of a cone = πr2 + πrs, where, 'r' is the radius, 's' is the slant height, and 'h' is the height of the cone.

5. Following the concepts of RD Sharma Class 9 Chapter 20 Maths, what is the difference between height and slant height?

The "height" of a cone and the "slant height" of a cone are two different things. Height or the altitude of a cone is referred to as its vertical height, ie. Ax2 + Bx2 = Cx2 can be used to calculate the slant height. In this formula, a represents the altitude, b represents the angle between the centre of the base and the starting point of the slant height segment, and c represents the slant height. This is the distance perpendicular to the cone's top from the base of the cone to the top. A cone's slant height is the height at which the side of the cone meets the edge of its circular base.