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142 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Truncated Cone
A truncated cone consists of two surfaces, two circular bases, and a curved surface. The curved surface area represents the lateral surface of the truncated cone. For example, consider a lampshade. The fabric part of the lampshade is the curved surface, and its area is equal to the lateral surface area of the truncated cone. The top and bottom circular bases are not part of the lateral surface area.
What is the Lateral Surface Area of a Truncated Cone?
The curved surface area of the truncated cone is considered the lateral surface area of a truncated cone.
This is the surface area that wraps around the sides of the cone, excluding the top and bottom bases.
Formula for Lateral Surface Area of a Truncated Cone
How to Find Lateral Surface Area of a Truncated Cone
To find the lateral surface area of a truncated cone, follow these steps:
Step 1: Take note of the given parameters, namely, the radii of the two bases and the slant height.
Step 2: Ensure that all the measurements are in the same unit before calculation.
Step 3: Use the equation, Area = π(R + r)l, to find the lateral surface area of the truncated cone.
Step 4: Provide the calculated answer in square units.
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Common Mistakes and How to Avoid Them in the Lateral Surface Area of a Truncated Cone
There are a few typical mistakes people make while calculating the lateral surface area of a truncated cone. Some of them are listed below:
Mistake 1
Confusing the slant height with the height of the truncated cone.
The slant height (l) is the distance along the side of the cone between the two bases, while the height (h) is the perpendicular distance between the two bases.
Mistake 2
Incorrectly using the radii in the formula.
Ensure you use both the larger and smaller radii (R and r) correctly in the formula.
Double-check your substitutions before finalizing the answer.
Mistake 3
Not mentioning the units with the numerical value.
It's important to mention the unit with the answer, even if the question doesn't specify the unit.
It's preferable to write “square units” as a unit for the standard representation of a value.
Mistake 5
Confusing lateral surface area with total surface area.
Lateral surface area refers only to the curved surface between the two bases, whereas total surface area includes the areas of both the curved surface and the two circular bases.
Solved Examples on Lateral Surface Area of a Truncated Cone
Problem 1
What is the lateral surface area of a truncated cone with a larger base radius = 8 cm, a smaller base radius = 5 cm, and a slant height = 10 cm?
408.4 cm²
Explanation
Given: Larger base radius (R) = 8 cm, Smaller base radius (r) = 5 cm, Slant height (l) = 10 cm
LSA = π(R + r)l = 3.14×(8 + 5)×10 = 408.4 cm²
Problem 2
If a truncated cone has a slant height of 6 cm, a larger base radius of 10 cm, and a lateral surface area of 301.44 cmยฒ, find the radius of the smaller base.
5 cm
Explanation
Given: Larger base radius (R) = 10 cm, Slant height (l) = 6 cm, LSA = 301.44 cm²
Using the formula: LSA = π(R + r)l
301.44 = 3.14×(10 + r)×6
Simplifying gives: 301.44 = 18.84×(10 + r)
10 + r = 301.44/18.84
10 + r = 16
r = 16 - 10
r = 5 cm
Problem 3
Calculate the lateral surface area of a truncated cone with larger base radius of 7 cm, smaller base radius of 3 cm, and slant height of 9 cm.
565.2 cm²
Explanation
Given: Larger base radius R = 7 cm, Smaller base radius r = 3 cm, Slant height l = 9 cm
LSA = π(R + r)l = 3.14×(7 + 3)×9 = 565.2 cm²
Problem 4
Evaluate the slant height of a truncated cone if its larger base radius is 12 units, its smaller base radius is 8 units, and its lateral surface area is 628 square units (Use ฯ = 3.14).
10 units
Explanation
Given: Larger base radius (R) = 12 units, Smaller base radius (r) = 8 units, Lateral surface area = 628 square units
Using the formula: LSA = π(R + r)l
628 = 3.14×(12 + 8)×l
628 = 3.14×20×l
628 = 62.8×l
l = 628/62.8
l = 10 units
Problem 5
Find the smaller base radius of a truncated cone if its larger base radius is 9 cm, the slant height is 15 cm, and its lateral surface area is 706.5 cmยฒ (Use ฯ = 3.14).
6 cm
Explanation
Let the smaller base radius be “r” cm. Given: Larger base radius R = 9 cm, Slant height l = 15 cm, LSA = 706.5 cm²
Using the formula: LSA = π(R + r)l
706.5 = 3.14×(9 + r)×15
706.5 = 47.1×(9 + r)
9 + r = 706.5/47.1
9 + r = 15
r = 15 - 9
r = 6 cm
FAQs on Lateral Surface Area of a Truncated Cone
1.What is Lateral Surface Area of a Truncated Cone?
2.How to calculate the lateral surface area of a truncated cone?
3.Is the lateral surface area and the curved surface area the same?
4.What is the relation between slant height and height of a truncated cone?
5.How does the lateral surface area change if the radii are doubled?
Important Glossary for Lateral Surface Area of a Truncated Cone
- Slant height: The length between the edges of the two bases along the side of the truncated cone.
- Truncated cone: A cone with the top portion cut off, having two circular bases of different radii.
- Larger base radius (R): The radius of the larger circular base of the truncated cone.
- Smaller base radius (r): The radius of the smaller circular base of the truncated cone.
- Lateral surface area: The area of the curved surface between the two circular bases of a truncated cone.
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
