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)
This question appeared on the ETEA MDCAT 2011 paper, which you can sit online with every answer explained.
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