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If the surface area of a solid sphere is 1386 cm2. then the total surface area of the solid hemisphere of the same radius is
- a)1039.5 cm2.
- b)1559.25 cm2.
- c)519.75 cm2.
- d)693 cm2.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the surface area of a solid sphere is 1386cm2.then the total surfac...
Given: Surface Area of Solid Sphere = 1386 cm²
To find: Total Surface Area of Solid Hemisphere of same radius.
Let the radius of the sphere be ‘r’.
1. Surface Area of Sphere:
The surface area of a sphere is given by:
4πr²
Given, Surface Area of Sphere = 1386 cm²
4πr² = 1386
r² = 1386 / (4π)
r² = 110.25
r = √110.25
r = 10.5 cm
2. Surface Area of Hemisphere:
The surface area of a hemisphere is given by:
2πr²
Given, Radius of Hemisphere = 10.5 cm
Surface Area of Hemisphere = 2π(10.5)²
Surface Area of Hemisphere = 2π(110.25)
Surface Area of Hemisphere = 2 x 110.25 x 22/7
Surface Area of Hemisphere = 693 cm²
3. Total Surface Area of Solid Hemisphere:
The total surface area of a solid hemisphere is given by:
3πr²
Total Surface Area of Solid Hemisphere = 3π(10.5)² / 2
Total Surface Area of Solid Hemisphere = 3 x 110.25 x 22/7 / 2
Total Surface Area of Solid Hemisphere = 346.5 cm²
Therefore, the correct option is A) 1039.5 cm².
To find: Total Surface Area of Solid Hemisphere of same radius.
Let the radius of the sphere be ‘r’.
1. Surface Area of Sphere:
The surface area of a sphere is given by:
4πr²
Given, Surface Area of Sphere = 1386 cm²
4πr² = 1386
r² = 1386 / (4π)
r² = 110.25
r = √110.25
r = 10.5 cm
2. Surface Area of Hemisphere:
The surface area of a hemisphere is given by:
2πr²
Given, Radius of Hemisphere = 10.5 cm
Surface Area of Hemisphere = 2π(10.5)²
Surface Area of Hemisphere = 2π(110.25)
Surface Area of Hemisphere = 2 x 110.25 x 22/7
Surface Area of Hemisphere = 693 cm²
3. Total Surface Area of Solid Hemisphere:
The total surface area of a solid hemisphere is given by:
3πr²
Total Surface Area of Solid Hemisphere = 3π(10.5)² / 2
Total Surface Area of Solid Hemisphere = 3 x 110.25 x 22/7 / 2
Total Surface Area of Solid Hemisphere = 346.5 cm²
Therefore, the correct option is A) 1039.5 cm².
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Community Answer
If the surface area of a solid sphere is 1386cm2.then the total surfac...
Surface area of sphere = 4πr²
1386 = 4πr²
1386 ÷4 =22/7 r²
346.5 cm = 22 /7 r²
(346.5 x 7 ) ÷ 22 = r²
110.25 = r²
√110.25 = r²
10.5 = r
total surface area of hemisphere = 3πr²
3 x 22 /7 x 10.5 x 10.5
= 1039.5 cm²
...
simpler form
T.S.A Of sphere = 4πr²
1386 cm² = 4πr²
1386 ÷ 4 = πr²
346.5 = πr²
....
T.S.A of hemisphere = 3πr²
= 3 x 346.5
= 1039.5 cm
1386 = 4πr²
1386 ÷4 =22/7 r²
346.5 cm = 22 /7 r²
(346.5 x 7 ) ÷ 22 = r²
110.25 = r²
√110.25 = r²
10.5 = r
total surface area of hemisphere = 3πr²
3 x 22 /7 x 10.5 x 10.5
= 1039.5 cm²
...
simpler form
T.S.A Of sphere = 4πr²
1386 cm² = 4πr²
1386 ÷ 4 = πr²
346.5 = πr²
....
T.S.A of hemisphere = 3πr²
= 3 x 346.5
= 1039.5 cm
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If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer?
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If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer?.
If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the surface area of a solid sphere is 1386cm2.then the total surface area of the solid hemisphere of the same radius isa)1039.5cm2.b)1559.25cm2.c)519.75cm2.d)693cm2.Correct answer is option 'A'. Can you explain this answer?.
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