Answer:
Step-by-step explanation:
The regular polygons that can be used to form a regular tessellation are an equilateral triangle, a square, and a regular hexagon.
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Consider the top half of a sphere centered at the origin with radius

, which can be described by the equation

and consider a plane

with

. Call the region between the two surfaces

. The volume of

is given by the triple integral

Converting to polar coordinates will help make this computation easier. Set

Now, the volume can be computed with the integral

You should get
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