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Spherical wedge - mklabgr - 07-27-2026
![[Image: Sphericalwedge-300x291.png]](https://media.geeksforgeeks.org/wp-content/uploads/20220412223120/Sphericalwedge-300x291.png)
Spherical wedge
Summary
A spherical wedge (also called an ungula) is the three-dimensional region of a sphere enclosed by two plane semidisks that meet along a common diameter and the curved surface between them, known as a spherical lune. It can be visualized as a slice of an orange cut through its centre, where the size of the slice is determined by the dihedral angle between the two bounding planes.
The wedge occupies the same fraction of the sphere’s volume and surface area as its angle occupies of a full revolution ($360°$ or $(2\pi)$ radians). Consequently, its volume is ($V=\frac{2}{3}\alpha r^3$) and the area of its curved spherical lune is ($A=2\alpha r^2$), where ® is the sphere’s radius and ($\alpha$) is the angle in radians.
A wedge with an angle of ($180^\circ$) forms a hemisphere, while an angle of ($360^\circ$) corresponds to the entire sphere. Spherical wedges are important in geometry because they provide a simple way to partition spheres and derive proportional relationships for volume and surface area.
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