CSA of Cone: Cone is a three-dimensional shape having a circular base connecting to a point called an apex or vertex. A cone has a circular cross-section, unlike a pyramid which has a triangular cross-section. The curved surface area (CSA) is the total area occupied by the cone in a three-dimensional plane. Therefore, the curved surface area of a cone is equal to the product of the radius of the circular base and the slant height of the cone. There are two types of cones – right circular cone and oblique cone.

Students learn the concept of the curved surface area of cones in secondary classes to solve geometrical problems easily. Check NCERT Solutions for Class 9 Maths Chapter 13 for a better understanding. The detailed information on the Cone CSA formula is provided in this article. Read more to know how to find the CSA of cone, with help of formula and solved examples.

CSA of Cone: Definition

The curved surface of cone is a total area occupied by the cone in a three-dimensional plane. Cone is a three-dimensional shape with a circular base that narrows down from a flat surface to a point known as the apex or vertex. CSA of the cone is equal to the product of the radius of the base and the height of the cone.

The distance between the flat surface and apex is called the height of the cone. The circular base of the cone is measured in radius. To calculate the CSA of cone formula is derived based on the radius and height of the cone. The derivation of the Surface area of cone is shown in this article.

Properties of Cone

1. It has only one base with one vertex.
2. It does not have an edge.
3. It is a three-dimensional shape.
4. The volume of cone is ⅓ πr²h.
5. The total surface area of cone is πr(l + r).

Surface Area of a Cone Formula

The Cone CSA formula is the product of the radius of the circular base and slant height of the cone. The CSA of Cone formula used to calculate the curved surface area of a cone is as follows:

Curved Surface Area (CSA) = πrl

Where r is the radius of the circular base and l is the slant height of the cone.

The Surface area of Right Circular Cone can be calculated similarly.

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Curved Surface Area of a Cone Solved Examples

Below we have provided some of the solved examples of Curved Surface Area of a Cone for your reference:

Example 1: Find the curved surface area of a cone whose base radius is 8 cm and slant height is 16 cm.
Solution: Curved surface area of a cone = πrl

= 3.14× 8×16
=  402 cm²

Therefore, the curved surface area of a cone is 402 cm².

Example 2: Find the curved surface area of a cone whose base radius is 6cm and slant height is 12 cm. Solution: Curved surface area of a cone = πrl

= 3.14× 6×12
=  226 cm²

Therefore, the curved surface area of a cone is 226 cm².

Download NCERT Solutions for Class 9 Maths Chapter 13 PDF

Slant Height of Cone

The distance between the vertex and the edge of the circular base of the cone is the slant height of the cone. The vertical height of a cone is the distance between the vertex and the circular base’s centre. The formula for calculating the slant height of a cone is:

Slant height of the cone, L = √(h²+r²)

where ‘h’ is the vertical height and ‘r’ is the radius of circular base of cone.

FAQs on CSA of Cone

We have provided some frequently asked questions on the CSA of a cone here:

Q.1: What is the formula of CSA of Cone?
Ans: The CSA of cone is equal to the product of the radius of the circular base and slant height of the cone. The formula of CSA of Cone is πrl.

Q.2: What is surface area of a Cone?
Ans: The curved surface area of a cone is the area occupied by the circular base of the cone.

Q.3: Define the height of the cone.
Ans: The distance between the flat surface and apex is called the height of the cone.

Q.4: What are the real-life examples of the cone?
Ans: A real-life example of the cone is a birthday hat, ice cream cone, funnel, Christmas tree etc.

Q.5: What is the volume of a cone?
Ans: The volume of a cone is ⅓ πr²h.

Q.6: Describe the properties of Cone?
Ans: The properties of Cone are as follows:
1. It has only one base with one vertex.
2. It does not have an edge.
3. It is a three-dimensional shape.

Now you are provided with all the crucial information about the CSA of Cone. Practice more questions and have a firm grip on this concept. Students can refer to the NCERT Solutions for Maths provided by Embibe to score good marks in their exams.

Get Maths formulas for Class 6 to 12 below:

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