The angle subtended at the centre of a sphere by its surface area is equal to:
Correct answer: D. 4 π streradian
- A. 4/3 π radian
- B. 4/3 π steradian
- C. 4 π radian
- D. 4 π streradian
Explanation
One steradian is the solid angle of a sphere subtended by a portion of the surface whose area is equal to the square of the sphere's radius. The complete surface area of a sphere= 4πr² so the total solid angle about a point = 4πr²/r² = 4π steradian The steradian is the unit of solid angles. It is used in 3D geometry. Whereas the radian is used in planar geometry so options A and C are ruled out as we are dealing with a 3D cone here. (The mention of surface area in the question implies that 3D geometry is involved)
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