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The solid angle subtended at the centre of a hemisphere of radius r will be:
- a)2π r
- b)2π
- c)4π
- d)2π / r
Correct answer is option 'B'. Can you explain this answer?
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The solid angle subtended at the centre of a hemisphere of radius r wi...
Solid angle is the angle subtended at a point in space by an area, i.e. angle enclosed in the volume formed by numerous lines lying on the surface and meeting at the point. It is usually denoted by symbol ‘ω’ and it is measured in steradian.
Area of the hemisphere = 2πr2
The solid angle subtended at the centre of a hemisphere of radius r will be
Most Upvoted Answer
The solid angle subtended at the centre of a hemisphere of radius r wi...
Π steradians.
The solid angle subtended at the centre of a hemisphere of radius r can be calculated as follows:
The hemisphere can be divided into infinitesimally small cones with their vertices at the centre of the hemisphere. The solid angle subtended by each cone can be calculated using the formula:
Ω = 2π(1 - cos(θ/2))
where θ is the cone's half-angle, which is equal to the angle between the two radii that form the cone's base.
For the cone at the top of the hemisphere, θ = π/2 and the solid angle subtended is:
Ω = 2π(1 - cos(π/4)) = 2π(1 - 1/√2) ≈ 1.58 steradians.
For all the other cones, θ < π/2="" and="" the="" solid="" angle="" subtended="" is="" less="" than="" that="" of="" the="" cone="" at="" the="" top="" of="" the="" hemisphere.="" as="" the="" number="" of="" cones="" approaches="" infinity,="" the="" sum="" of="" their="" solid="" angles="" approaches="" the="" solid="" angle="" of="" the="" entire="" hemisphere,="" which="" />
Ω = lim(n→∞) ΣΩ = lim(n→∞) n×2π(1 - cos(θ/2)) ≈ 2π steradians.
Therefore, the solid angle subtended at the centre of a hemisphere of radius r is approximately 2π steradians.
The solid angle subtended at the centre of a hemisphere of radius r can be calculated as follows:
The hemisphere can be divided into infinitesimally small cones with their vertices at the centre of the hemisphere. The solid angle subtended by each cone can be calculated using the formula:
Ω = 2π(1 - cos(θ/2))
where θ is the cone's half-angle, which is equal to the angle between the two radii that form the cone's base.
For the cone at the top of the hemisphere, θ = π/2 and the solid angle subtended is:
Ω = 2π(1 - cos(π/4)) = 2π(1 - 1/√2) ≈ 1.58 steradians.
For all the other cones, θ < π/2="" and="" the="" solid="" angle="" subtended="" is="" less="" than="" that="" of="" the="" cone="" at="" the="" top="" of="" the="" hemisphere.="" as="" the="" number="" of="" cones="" approaches="" infinity,="" the="" sum="" of="" their="" solid="" angles="" approaches="" the="" solid="" angle="" of="" the="" entire="" hemisphere,="" which="" />
Ω = lim(n→∞) ΣΩ = lim(n→∞) n×2π(1 - cos(θ/2)) ≈ 2π steradians.
Therefore, the solid angle subtended at the centre of a hemisphere of radius r is approximately 2π steradians.
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The solid angle subtended at the centre of a hemisphere of radius r will be:a)2π rb)2πc)4πd)2π / rCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The solid angle subtended at the centre of a hemisphere of radius r will be:a)2π rb)2πc)4πd)2π / rCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solid angle subtended at the centre of a hemisphere of radius r will be:a)2π rb)2πc)4πd)2π / rCorrect answer is option 'B'. Can you explain this answer?.
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