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123 LearnersLast updated on August 29, 2025
Surface Area of Oblique Cone
An oblique cone is a 3-dimensional shape that has a circular base but with the apex not aligned directly above the center of the base. The surface area of an oblique cone is the total area covered by its outer surface. This includes both the curved surface and the base of the cone. In this article, we will learn about the surface area of an oblique cone.
What is the Surface Area of an Oblique Cone?
The surface area of an oblique cone is the total area occupied by the boundary or surface of the cone. It is measured in square units. Unlike a right circular cone, where the vertex aligns with the base's center, an oblique cone's vertex is offset, causing it to lean. The surface area of the oblique cone includes its curved surface area and the base area, similar to other cones.
Surface Area of an Oblique Cone Formula
An oblique cone has a curved surface and a base, resulting in two surface areas: the curved surface area and the total surface area.
Despite the tilt, the formulas for these areas remain similar to those of a right cone.
Curved Surface Area of an Oblique Cone Total Surface Area of an Oblique Cone
Curved Surface Area of an Oblique Cone
The area of the curved part of the oblique cone, excluding its base, is known as the curved surface area.
The formula for the CSA (Curved Surface Area) is the same:
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 an Oblique Cone
The total surface area includes both the curved surface and the base area.
While the cone is oblique, the calculation remains:
Total surface area = πr(r + l) square units
Where r is the radius of the base, and l is the slant height of the cone.
Volume of an Oblique Cone
The volume of an oblique cone shows how much space is inside it. Like a right cone, it is one-third of the volume of a cylinder with the same height and base.
The volume can be calculated as: Volume = ⅓(πr²h) cubic units
Confusion between CSA and TSA
Students may confuse the curved surface area (CSA) and the total surface area (TSA) of an oblique cone.
Remember, CSA involves only the curved part, while TSA includes both the curved surface and the base.
Mistake 1
Using height instead of slant height
Students might use the vertical height instead of the slant height when calculating the curved surface area. Always use the slant height (l) in the formula: CSA = πrl.
Mistake 2
Using the wrong value for π
It's common to mistakenly use 22 as the value of π. Use accurate values like 22/7 or 3.14 for precision in calculations.
Mistake 3
Forgetting to include the base area in the total surface area
Some students calculate only the curved surface, omitting the base area. Always include both when calculating TSA: TSA = CSA + base area.
Mistake 4
Assuming curved surface area and lateral surface area are different
In cones, the curved surface area and the lateral surface area are the same, so use the same formula.
Mistake 5
Solved Examples of Surface Area of Oblique Cone
Find the curved surface area of an oblique cone with a radius of 6 cm and a slant height of 9 cm.
CSA = 169.56 cm²
Problem 1
Given r = 6 cm, l = 9 cm. Use the formula: CSA = πrl = 3.14 × 6 × 9 = 169.56 cm²
Find the total surface area of an oblique cone with a radius of 4 cm and a slant height of 12 cm.
Explanation
TSA = 201.06 cm²
Problem 2
Use the formula: TSA = πr(r + l) = 3.14 × 4 × (4 + 12) = 3.14 × 4 × 16 = 201.06 cm²
An oblique cone has a radius of 7 cm and a height of 10 cm. Find the total surface area.
Explanation
TSA = 350.44 cm²
Problem 3
Find the slant height using: l = √(r² + h²) = √(7² + 10²) = √(49 + 100) = √149 = 12.21 cm Use the TSA formula: TSA = πr(r + l) = 3.14 × 7 × (7 + 12.21) = 3.14 × 7 × 19.21 = 350.44 cm²
Find the curved surface area of an oblique cone with a radius of 5 cm and a slant height of 11 cm.
Explanation
CSA = 172.7 cm²
Problem 4
CSA = πrl = 3.14 × 5 × 11 = 172.7 cm²
The slant height of an oblique cone is 8 cm, and its curved surface area is 200 cm². Find the radius.
Explanation
Radius = 7.96 cm
It is the total area that covers the outside of the oblique cone, including its curved side and the base.
1.What are the two types of surface area in an oblique 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 an Oblique Cone
Students often make mistakes while calculating the surface area of an oblique cone, leading to incorrect answers. Below are some common mistakes and tips to avoid them.
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Seyed Ali Fathima S
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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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