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Needed a Document for Chapter 13 , exercise 13.4 , sum 3 with solutions?
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Needed a Document for Chapter 13 , exercise 13.4 , sum 3 with solution...
Chapter 13: Surface Areas and Volumes
Exercise 13.4: Question
Find the total surface area of a cone with radius 6 cm and height 8 cm. (Take π = 3.14)
Solution:
To find the total surface area of a cone, we need to calculate the curved surface area and the base area separately.
1. Curved Surface Area of Cone:
The curved surface area is the lateral surface area of the cone. It can be calculated using the formula:
Curved Surface Area = π * radius * slant height
To find the slant height, we can use the Pythagorean theorem:
slant height = √(height^2 + radius^2)
Given that the radius is 6 cm and the height is 8 cm, we can calculate the slant height:
slant height = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 cm
Now, we can calculate the curved surface area:
Curved Surface Area = π * 6 cm * 10 cm = 60π cm^2
2. Base Area of Cone:
The base area of the cone is simply the area of a circle with the radius of the cone.
Base Area = π * radius^2 = π * (6 cm)^2 = 36π cm^2
3. Total Surface Area of Cone:
The total surface area is the sum of the curved surface area and the base area.
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area = 60π cm^2 + 36π cm^2 = 96π cm^2
Therefore, the total surface area of the given cone is 96π cm^2.
Note: In this solution, the value of π is taken as 3.14. However, it is an approximated value.
Exercise 13.4: Question
Find the total surface area of a cone with radius 6 cm and height 8 cm. (Take π = 3.14)
Solution:
To find the total surface area of a cone, we need to calculate the curved surface area and the base area separately.
1. Curved Surface Area of Cone:
The curved surface area is the lateral surface area of the cone. It can be calculated using the formula:
Curved Surface Area = π * radius * slant height
To find the slant height, we can use the Pythagorean theorem:
slant height = √(height^2 + radius^2)
Given that the radius is 6 cm and the height is 8 cm, we can calculate the slant height:
slant height = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 cm
Now, we can calculate the curved surface area:
Curved Surface Area = π * 6 cm * 10 cm = 60π cm^2
2. Base Area of Cone:
The base area of the cone is simply the area of a circle with the radius of the cone.
Base Area = π * radius^2 = π * (6 cm)^2 = 36π cm^2
3. Total Surface Area of Cone:
The total surface area is the sum of the curved surface area and the base area.
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area = 60π cm^2 + 36π cm^2 = 96π cm^2
Therefore, the total surface area of the given cone is 96π cm^2.
Note: In this solution, the value of π is taken as 3.14. However, it is an approximated value.
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Needed a Document for Chapter 13 , exercise 13.4 , sum 3 with solution...
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Needed a Document for Chapter 13 , exercise 13.4 , sum 3 with solutions? Related: Full Chapter Exercise Solutions(Hindi)- Surface Area and Volumes? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Needed a Document for Chapter 13 , exercise 13.4 , sum 3 with solutions? Related: Full Chapter Exercise Solutions(Hindi)- Surface Area and Volumes? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Needed a Document for Chapter 13 , exercise 13.4 , sum 3 with solutions? Related: Full Chapter Exercise Solutions(Hindi)- Surface Area and Volumes?.
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