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# Spherical Wedge and Spherical Lune Formula

A solid formed by revolving a semicircle about its diameter with less than 360 degrees, then it is called a spherical wedge. Spherical lune is the area on a sphere surrounded by two half circles that meet at antipodal points.When we say antipodal, we mean it is the point on the surface of a sphere which is diametrically opposite to it. If we draw a line from one point to another then it will form a straight line. The formula for spherical wedge is to calculate volume, arc length and surface area.

The formulas are:

$\large Volume=\frac{2}{3}\:R^{3}\theta$

$\large Surface\;Area=2R^{2}\theta$

$\large Arc\;Length\;at\;the\;equator=R\theta$

### Solved Example

Question: Find the volume of the spherical wedge with radius 8 m and the dihedral angle of the wedge 45 degrees ?

Solution:

Given,
R = 8 m
Using the formula: $Volume=\frac{2}{3}\:R^{3}\theta$
$Volume=\frac{2}{3}\times 8^{3}\times \frac{\pi}{4}$
$=268\;m^{3}$