# Spherical Wedge and Spherical Lune

A spherical wedge is a solid formed by revolving a semi-circle about its diameter by less than 360°. Spherical Lune is the curve surface of the wedge, it is a surface formed by revolving a semi-circular arc about its diameter by less than 360°.

**Formula for Spherical Wedge and Lune**

The formula for spherical wedge and Lune can be found by ratio and proportion, meaning, spherical wedge is similar to the sphere and spherical Lune is similar to spherical surface.

**Volume of wedge, V _{wedge}**

Volume of wedge / central angle = Volume of sphere / 1 revolution

$\dfrac{V_{wedge}}{\theta_{deg}} = \dfrac{\frac{4}{3}\pi R^3}{360^\circ}$

$V_{wedge} = \frac{2}{3} R^3 \theta_{rad}$

**Area of Lune, A _{lune}**

Area of Lune / central angle = Area of sphere / 1 revolution

$\dfrac{A_{lune}}{\theta_{deg}} = \dfrac{4\pi R^2}{360^\circ}$

$A_{lune} = 2 R^2 \theta_{rad}$