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A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .?
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A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere...
To find the total surface area of the toy, which consists of a cone mounted on a hemisphere, we need to calculate the surface areas of both shapes and then combine them.
Total Height of the Toy
- The total height of the toy is given as 15.5 cm.
- The radius of both the cone and the hemisphere is 3.5 cm.
Height of the Cone
- The height of the hemisphere is equal to its radius, which is 3.5 cm.
- Therefore, the height of the cone can be calculated as:
- Height of the cone = Total height - Height of the hemisphere
- Height of the cone = 15.5 cm - 3.5 cm = 12 cm
Surface Area Calculations
1. Surface Area of the Hemisphere
- The formula for the curved surface area of a hemisphere is:
- CSA = 2 * π * r²
- Substituting the radius:
- CSA of hemisphere = 2 * π * (3.5)² = 24.5π cm²
2. Surface Area of the Cone
- The formula for the curved surface area of a cone is:
- CSA = π * r * l, where l is the slant height.
- To find the slant height (l):
- l = √(r² + h²) = √((3.5)² + (12)²) = √(12.25 + 144) = √156.25 = 12.5 cm
- Thus, the CSA of the cone:
- CSA of cone = π * (3.5) * (12.5) = 43.75π cm²
Total Surface Area of the Toy
- To find the total surface area:
- Total Surface Area = CSA of hemisphere + CSA of cone
- Total Surface Area = 24.5π + 43.75π = 68.25π cm²
Final Result
- The total surface area of the toy is approximately 214.6 cm² (using π ≈ 3.14).
Total Height of the Toy
- The total height of the toy is given as 15.5 cm.
- The radius of both the cone and the hemisphere is 3.5 cm.
Height of the Cone
- The height of the hemisphere is equal to its radius, which is 3.5 cm.
- Therefore, the height of the cone can be calculated as:
- Height of the cone = Total height - Height of the hemisphere
- Height of the cone = 15.5 cm - 3.5 cm = 12 cm
Surface Area Calculations
1. Surface Area of the Hemisphere
- The formula for the curved surface area of a hemisphere is:
- CSA = 2 * π * r²
- Substituting the radius:
- CSA of hemisphere = 2 * π * (3.5)² = 24.5π cm²
2. Surface Area of the Cone
- The formula for the curved surface area of a cone is:
- CSA = π * r * l, where l is the slant height.
- To find the slant height (l):
- l = √(r² + h²) = √((3.5)² + (12)²) = √(12.25 + 144) = √156.25 = 12.5 cm
- Thus, the CSA of the cone:
- CSA of cone = π * (3.5) * (12.5) = 43.75π cm²
Total Surface Area of the Toy
- To find the total surface area:
- Total Surface Area = CSA of hemisphere + CSA of cone
- Total Surface Area = 24.5π + 43.75π = 68.25π cm²
Final Result
- The total surface area of the toy is approximately 214.6 cm² (using π ≈ 3.14).
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A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .?
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A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .? 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 A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .?.
A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .? 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 A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius . The total height of the toy is 15.5cm . Find the total surface area of the toy .?.
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