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The surface area of the segment of a sphere of radius a and height h is given by:
- a)2πh
- b)2πah
- c)2πa2h
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The surface area of the segment of a sphere of radius a and height h i...
Let the sphere be generated by the revolution about the x - axis of the circle
x2 + y2=a2 ...(i)
Let OA =a, OC = b and OB = b + h
Hence The required surface
x2 + y2=a2 ...(i)
Let OA =a, OC = b and OB = b + h
Hence The required surface
Most Upvoted Answer
The surface area of the segment of a sphere of radius a and height h i...
Let the sphere be generated by the revolution about the x - axis of the circle
x2 + y2=a2 ...(i)
Let OA =a, OC = b and OB = b + h
Hence The required surface
x2 + y2=a2 ...(i)
Let OA =a, OC = b and OB = b + h
Hence The required surface
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The surface area of the segment of a sphere of radius a and height h i...
Surface Area of a Segment of a Sphere
To find the surface area of a segment of a sphere, we can start by understanding the geometry of the segment. The segment can be visualized as a slice of the sphere with a flat base. The formula for the surface area of a segment of a sphere is:
2πah
Where:
- a = radius of the sphere
- h = height of the segment
Explanation
- The formula 2πah represents the lateral surface area of the segment, which is the curved part of the segment.
- The factor 2πa corresponds to the circumference of the base of the segment, which is a circle with radius a.
- The height h of the segment determines the length of the lateral surface area, as it represents the distance from the base to the top of the segment.
Therefore, the correct answer to the given question is option B, which corresponds to the formula 2πah for the surface area of the segment of a sphere.
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