102 LearnersLast updated on 30 August 2025
Surface Area of Cylinder and Cone
A cylinder and a cone are both 3-dimensional shapes with circular bases. The surface area of these shapes is the total area covered by their outer surfaces. The surface area of a cylinder includes its two circular bases and its curved surface, while the surface area of a cone includes its curved surface and its base. In this article, we will learn about the surface area of both a cylinder and a cone.
What is the Surface Area of a Cylinder and a Cone?
The surface area of a cylinder and a cone is the total area occupied by their boundaries or surfaces.
It is measured in square units. A cylinder is a 3D shape with two parallel circular bases and a curved surface connecting them.
A cone, on the other hand, has a single circular base and a curved surface that tapers to a point called the vertex.
Cylinders have three surface areas: two base areas and a curved surface area.
Cones have two surface areas: the curved surface area and the total surface area.
Surface Area Formulas for Cylinder and Cone
Both cylinders and cones have curved surfaces, and they have formulas to calculate their surface areas.
Look below to see their surface areas, heights, slant heights, and radii.
A cylinder has three surface areas:
Curved Surface Area of a Cylinder
Total Surface Area of a Cylinder
A cone has two surface areas: Curved Surface Area of a Cone
Total Surface Area of a Cone
Curved Surface Area of a Cylinder
The curved surface area of a cylinder is the area of its outer curved surface, excluding the bases.
The formula for the curved surface area (CSA) of the cylinder is given as:
Curved Surface Area = 2πrh square units
Here, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Total Surface Area of a Cylinder
The total surface area of a cylinder includes the area of the curved surface and the area of the two circular bases.
It is calculated using the formula:
Total Surface Area = 2πr(r + h) square units
Where r is the radius of the base of the cylinder, and h is its height.
Curved Surface Area of a Cone
The area of the curved part of the cone, excluding its base, is known as the curved surface area of a cone.
The curved surface area of the cone is also called the lateral surface area.
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 the cone, and l is the slant height of the cone.
Total Surface Area of a Cone
The total area occupied by the cone, including the area of the curved surface and the area of the circular base, is known as the total surface area of the cone.
The total surface area of a cone is calculated by using the formula:
Total Surface Area = πr(r + l) square units Where r is the radius of the base of the cone, and l is the slant height of the cone.
Confusion between Surface Areas
Students sometimes mix up the formulas for the curved surface area and the total surface area of both cylinders and cones. Always remember that the curved surface area excludes the bases, while the total surface area includes them.
Mistake 1
Using Height Instead of Slant Height in Cones
Some students mistakenly use the vertical height instead of the slant height when calculating the curved surface area of a cone. Remember, the formula for the curved surface area of a cone is πrl, so always use the slant height.
Mistake 2
Using the Wrong Value for π
A common mistake is using an incorrect value for π. Use accurate values like 22/7 or 3.14 for π to ensure precise calculations.
Mistake 3
Forgetting to Include Base Areas in Total Surface Area
Students often calculate only the curved surface and forget to add the base areas for the total surface area. Make sure to include both parts when calculating the total surface area.
Mistake 4
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 both cylinders and cones, they mean the same thing. Use the same formula for both.
Mistake 5
Solved Examples of Surface Area of Cylinder and Cone
Find the curved surface area of a cylinder with a radius of 4 cm and a height of 12 cm.
CSA = 301.44 cm²
Problem 1
Given r = 4 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 4 × 12 = 301.44 cm²
Find the total surface area of a cylinder with a radius of 5 cm and a height of 10 cm.
Explanation
TSA = 471 cm²
Problem 2
Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 10) = 2 × 3.14 × 5 × 15 = 471 cm²
A cone has a radius of 6 cm and a slant height of 10 cm. Find the curved surface area.
Explanation
CSA = 188.4 cm²
Problem 3
Use the formula: CSA = πrl = 3.14 × 6 × 10 = 188.4 cm²
Find the total surface area of a cone with a radius of 7 cm and a slant height of 14 cm.
Explanation
TSA = 462 cm²
Problem 4
Use the formula: TSA = πr(r + l) = 3.14 × 7 × (7 + 14) = 3.14 × 7 × 21 = 462 cm²
The slant height of a cone is 12 cm, and its curved surface area is 120 cm². Find the radius.
Explanation
Radius = 3.18 cm
It is the total area that covers the outside of the cylinder or cone, including their curved surfaces and bases.
1.What are the two types of surface areas in a cone and a cylinder?
2.What is the difference between slant height and height in a cone?
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 Cylinder and Cone
Students often make mistakes while calculating the surface area of cylinders and cones, leading to incorrect answers. Below are some common mistakes and how to avoid them.
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.
Fun Fact
: She has songs for each table which helps her to remember the tables
