RD Sharma Class 9 Solutions Chapter 20 - Surface Area and Volume of Right Circular Cone (Ex 20.2) Exercise 20.2 - Free PDF
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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.
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.
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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)
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)
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?
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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:
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
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.