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Which one of the following statements is correct? For a hemisphere, the solid angle is measured.
- a)In radian and its maximum value is π
- b)In degree and its maximum value is 180°
- c)In steradian and its maximum value is 2 π
- d)In steradian and its maximum value is π
Correct answer is option 'C'. Can you explain this answer?
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Which one of the following statements is correct? For a hemisphere, th...
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Which one of the following statements is correct? For a hemisphere, th...
Statement: For a hemisphere, the solid angle is measured.
a) In radian and its maximum value is
b) In degree and its maximum value is 180
c) In steradian and its maximum value is 2
d) In steradian and its maximum value is
Correct answer: option 'C' (In steradian and its maximum value is 2)
Explanation:
1. Solid Angle:
Solid angle is a measure of how much of the surrounding space is covered by a given object. It is analogous to the concept of angle in two dimensions, but in three dimensions. Solid angle is measured in steradians (sr).
2. Hemisphere:
A hemisphere is a three-dimensional shape that is half of a sphere. It has a curved surface and a flat circular base. The hemisphere is symmetrical about its base and has a maximum height equal to the radius of the base.
3. Solid Angle of a Hemisphere:
The solid angle of a hemisphere is the measure of the amount of space it covers from a specific point in three dimensions. Since a hemisphere is a three-dimensional object, the solid angle is measured in steradians (sr).
4. Maximum Value of Solid Angle:
The maximum value of the solid angle for a hemisphere can be determined by considering the entire surface area of the hemisphere. The hemisphere has a total surface area of 2πr^2, where r is the radius of the base.
To find the solid angle, we divide the surface area by the square of the radius. Therefore, the maximum value of the solid angle for a hemisphere is given by:
Solid Angle = Surface Area / (r^2)
For a hemisphere, the surface area is equal to half the surface area of a sphere, which is 2πr^2. Thus, the maximum value of the solid angle for a hemisphere is:
Solid Angle = (2πr^2) / (r^2)
Solid Angle = 2π
Conclusion:
Therefore, the correct statement is option 'C' that states the solid angle of a hemisphere is measured in steradians (sr) and its maximum value is 2 (2π when expressed in terms of π).
a) In radian and its maximum value is
b) In degree and its maximum value is 180
c) In steradian and its maximum value is 2
d) In steradian and its maximum value is
Correct answer: option 'C' (In steradian and its maximum value is 2)
Explanation:
1. Solid Angle:
Solid angle is a measure of how much of the surrounding space is covered by a given object. It is analogous to the concept of angle in two dimensions, but in three dimensions. Solid angle is measured in steradians (sr).
2. Hemisphere:
A hemisphere is a three-dimensional shape that is half of a sphere. It has a curved surface and a flat circular base. The hemisphere is symmetrical about its base and has a maximum height equal to the radius of the base.
3. Solid Angle of a Hemisphere:
The solid angle of a hemisphere is the measure of the amount of space it covers from a specific point in three dimensions. Since a hemisphere is a three-dimensional object, the solid angle is measured in steradians (sr).
4. Maximum Value of Solid Angle:
The maximum value of the solid angle for a hemisphere can be determined by considering the entire surface area of the hemisphere. The hemisphere has a total surface area of 2πr^2, where r is the radius of the base.
To find the solid angle, we divide the surface area by the square of the radius. Therefore, the maximum value of the solid angle for a hemisphere is given by:
Solid Angle = Surface Area / (r^2)
For a hemisphere, the surface area is equal to half the surface area of a sphere, which is 2πr^2. Thus, the maximum value of the solid angle for a hemisphere is:
Solid Angle = (2πr^2) / (r^2)
Solid Angle = 2π
Conclusion:
Therefore, the correct statement is option 'C' that states the solid angle of a hemisphere is measured in steradians (sr) and its maximum value is 2 (2π when expressed in terms of π).
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Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer?
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Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer?.
Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer?.
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Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Which one of the following statements is correct? For a hemisphere, the solid angle is measured.a)In radian and its maximum value is πb)In degree and its maximum value is 180°c)In steradian and its maximum value is 2 πd)In steradian and its maximum value is πCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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