105 LearnersLast updated on August 5th, 2025
Surface Area of Cone Without Base
A cone is a 3-dimensional shape that has a circular base. The surface area of a cone without its base focuses only on the curved surface, known as the lateral surface area. This excludes the base area, providing the area of the slanted part of the cone. In this article, we will learn about the surface area of a cone without the base.
What is the Surface Area of a Cone Without Base?
The surface area of a cone without its base is the area occupied by the curved or lateral surface of the cone. It is measured in square units.
A cone is a 3D shape made by rotating a triangle around one of its sides. It has a round base at the bottom and a sharp point at the top called the vertex. When considering the surface area without the base, only the curved side is included.
Cones are classified into two types: right circular cones and oblique cones.
When the tip of the cone is exactly above the center of the base, it forms a neat, even shape called a right circular cone. If the vertex is not above the middle of the base and the cone leans to one side, then it is an oblique cone.
Surface Area of a Cone Without Base Formula
A cone has a curved surface, and when calculating the surface area without the base, only the curved surface area is considered.
Look at the cone below to see its surface area, height(h), slant height(l), and radius(r). A cone has one type of surface area without its base: Curved Surface Area of a Cone
Curved Surface Area of a Cone Without Base
The area of the curved part of the cone, excluding its base, is known as the curved surface area of a cone without base.
The formula for the CSA (Curved Surface Area) of the cone is given as: Curved Surface Area = 𝜋rl square units
Here, r is the radius of the base of a cone. l is the slant height of the cone.
Volume of a Cone
The volume of a cone shows how much space is inside it. It tells us how much space is inside the cone or how much it can hold. It is one-third of the volume of a cylinder with the same height and base.
The volume of a cone can be found by using the formula: Volume = ⅓ (𝜋r²h) cubic units
Confusion between CSA and TSA
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a cone are the same. This confusion arises because both involve the slant height and the radius. Always remember that CSA is used on only the curved side of the cone, and TSA includes the curved surface and the base.
Mistake 1
Using height instead of slant height
Some students mistakenly use the vertical height(h) instead of the slant height(l) when finding the curved surface area. Remember the formula for curved surface area is πrl, so always use the slant height.
Mistake 2
Using the wrong value for 𝜋
A common mistake of students is using 22 as the value of 𝜋. Instead, use accurate values like 22/7 or 3.14. 𝜋 is a special number in math, and using the correct value is important for getting the right answer.
Mistake 3
Assuming curved surface area and lateral surface area are different
Some students mistakenly believe that curved surface area and lateral surface area are different, but in a cone, they mean the same thing. So, use the same formula for both.
Mistake 4
Solved Examples of Surface Area of Cone Without Base
Find the curved surface area of a cone with a radius of 5 cm and a slant height of 12 cm.
CSA = 188.4 cm²
Problem 1
Given r = 5 cm, l = 12 cm. Use the formula: CSA = πrl = 3.14 × 5 × 12 = 3.14 × 60 = 188.4 cm²
Find the curved surface area of a cone with radius 4 cm and slant height 9 cm.
Explanation
CSA = 113.04 cm²
Problem 2
Use the formula: CSA = 𝜋rl = 3.14 × 4 × 9 = 3.14 × 36 = 113.04 cm²
A cone has a radius of 8 cm and a slant height of 15 cm. Calculate the curved surface area.
Explanation
CSA = 376.8 cm²
Problem 3
Use the CSA formula: CSA = 𝜋rl = 3.14 × 8 × 15 = 3.14 × 120 = 376.8 cm²
Find the curved surface area of a cone with radius 6 cm and slant height 14 cm.
Explanation
CSA = 263.76 cm²
Problem 4
CSA = 𝜋rl = 3.14 × 6 × 14 = 3.14 × 84 = 263.76 cm²
The slant height of a cone is 18 cm, and its curved surface area is 360 cm². Find the radius.
Explanation
Radius = 6.37 cm
It is the total area that covers just the curved side of the cone, excluding its base.
1.How do you calculate the curved surface area of a cone?
2.What is the difference between slant height and height?
3.Is curved surface area the same as lateral surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Cone Without Base
Students often make mistakes while calculating the curved surface area of a cone, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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: She has songs for each table which helps her to remember the tables
