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How to Find the Surface Area of a Spherical Segment

A spherical segment


The Surface of a Spherical Segment

The surface area of a spherical segment with height h and radius R is given by

A = 2πRh.

Note! Some books use the word spherical segment about the part of the sphere that looks like a hat, and not the one that looks like a belt. The formula for the area of the hat is exactly the same as for the belt, but in that case h is the height from the base of the hat and up to the top of the sphere, instead of the height from the center of the sphere up to the top of the segment.

Example 1

You have a sphere with a radius of 4. What is the surface area of the spherical segment with height h = 3?

You insert R = 4 and h = 3 into the formula and get

A = 2π 4 3 = 24π 75.4.

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