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Surface area formula for spherical cap A sphere of radius
Chapter 11, Problem 59E(choose chapter or problem)
A sphere of radius a is sliced parallel to the equatorial plane at a distance a - h from the equatorial plane (see figure). Find the general formula for the surface area of the resulting spherical cap (excluding the base) with thickness h.
Questions & Answers
QUESTION:
A sphere of radius a is sliced parallel to the equatorial plane at a distance a - h from the equatorial plane (see figure). Find the general formula for the surface area of the resulting spherical cap (excluding the base) with thickness h.
ANSWER:
Solution 59EStep 1 A sphere of radius a is sliced parallel to the equatorial plane at a distance of a – h from the equatorial plane.Need to find the general formula for the surface area of the resulting spherical cap.Consider the following figure: The blue colour portion surface area is to be determined.