Lateral Surface Area of a Truncated Cone
2026-02-28 12:47 Diff
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Last updated on December 11, 2025

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

We can find the lateral surface area of a truncated cone using the slant height “l”, the radius of the larger base “R”, and the radius of the smaller base “r”.

The lateral surface area is calculated by using the formula, Area = π(R + r)l, where l is the slant height of the 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:

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?

Okay, lets begin

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

Well explained 👍

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 cm², find the radius of the smaller base.

Okay, lets begin

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

Well explained 👍

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.

Okay, lets begin

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

Well explained 👍

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 π = 3.14).

Okay, lets begin

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

Well explained 👍

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 cm² (Use π = 3.14).

Okay, lets begin

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

Well explained 👍

FAQs on Lateral Surface Area of a Truncated Cone

1.What is Lateral Surface Area of a Truncated Cone?

The area consumed by the curved surface of a truncated cone, excluding the circular bases, is called the lateral surface area of a truncated cone.

2.How to calculate the lateral surface area of a truncated cone?

The lateral surface area of a truncated cone can be calculated using the formula: Area = π(R + r)l.

3.Is the lateral surface area and the curved surface area the same?

Yes, for a truncated cone, the terms lateral surface area and curved surface area are the same.

4.What is the relation between slant height and height of a truncated cone?

The slant height is the distance along the side of the truncated cone, while the height is the perpendicular distance between the two bases.

5.How does the lateral surface area change if the radii are doubled?

If both radii are doubled, the lateral surface area will not simply double; it is determined by the formula:

New LSA = π(2R + 2r)l = 2π(R + r)l, which doubles the original LSA.

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.

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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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