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:

$V o l u m e = \frac{2}{3} R^{3} θ$

$S u r f a c e A r e a = 2 R^{2} θ$

$A r c L e n g t h a t t h e e q u a t o r = R θ$

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
θ = π/4 radians

Using the formula:

\begin{array}{l} V o l u m e = \frac{2}{3} R^{3} θ \end{array}

\begin{array}{l} V o l u m e = \frac{2}{3} \times 8^{3} \times \frac{π}{4} \end{array}

\begin{array}{l} = 268 m^{3} \end{array}

Spherical Wedge and Spherical Lune Formula

Solved Example

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