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The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area?
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Understanding the Right Circular Cone
A right circular cone is a three-dimensional geometric figure with a circular base and a pointed top (vertex). The key dimensions involved in calculating the curved surface area are the slant height and radius.
Given Data
- Slant Height (l) = 10 m
- Height (h) = 8 m
Finding the Radius
To find the radius (r) of the cone, we can use the Pythagorean theorem. The relationship between slant height, height, and radius is given by:
- l² = r² + h²
Plugging in the values:
- 10² = r² + 8²
- 100 = r² + 64
- r² = 100 - 64 = 36
- r = √36 = 6 m
Curved Surface Area Formula
The formula to calculate the curved surface area (CSA) of a cone is:
- CSA = πrl, where r is the radius and l is the slant height.
Calculating the Curved Surface Area
Now, substituting the values into the formula:
- r = 6 m
- l = 10 m
Thus,
- CSA = π * 6 * 10
- CSA = 60π
Using π ≈ 3.14,
- CSA ≈ 60 * 3.14 ≈ 188.4 m²
Final Result
The curved surface area of the right circular cone is approximately 188.4 m². This area represents the surface that can be painted or covered.
A right circular cone is a three-dimensional geometric figure with a circular base and a pointed top (vertex). The key dimensions involved in calculating the curved surface area are the slant height and radius.
Given Data
- Slant Height (l) = 10 m
- Height (h) = 8 m
Finding the Radius
To find the radius (r) of the cone, we can use the Pythagorean theorem. The relationship between slant height, height, and radius is given by:
- l² = r² + h²
Plugging in the values:
- 10² = r² + 8²
- 100 = r² + 64
- r² = 100 - 64 = 36
- r = √36 = 6 m
Curved Surface Area Formula
The formula to calculate the curved surface area (CSA) of a cone is:
- CSA = πrl, where r is the radius and l is the slant height.
Calculating the Curved Surface Area
Now, substituting the values into the formula:
- r = 6 m
- l = 10 m
Thus,
- CSA = π * 6 * 10
- CSA = 60π
Using π ≈ 3.14,
- CSA ≈ 60 * 3.14 ≈ 188.4 m²
Final Result
The curved surface area of the right circular cone is approximately 188.4 m². This area represents the surface that can be painted or covered.
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The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area?
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The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area?.
The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The slant height of a right circular cone is 10 m and height is 8 m.find the curved surface area?.
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