Spherical Sector Formula

Spherical Sector Formula

A spherical sector is in a shape of an ice cream cone. Mathematically, the part of the sphere with vertex at the center and conical boundary is the spherical sector. The base of the sphere is called it’s zone. It can be the spherical cap and union of a cone. The formula we will use here is to find the volume and surface of the spherical sector.

The formula has been given below:

\[\large A=\pi r(2h+a)\]

\[\large V=\frac{2\pi r^{2}h}{3}\]

Solved example

Question: Find the volume of a sector of a sphere,the radius 8 cms and height of the cap is 10 cms ?


r = 8 cm
h = 10 cm

According to the formula:

\(\begin{array}{l}V=\frac{2\pi r^{2}h}{3}\end{array} \)
\(\begin{array}{l}V=\frac{2\times 3.14\times 8^{2}\times 10}{3}\end{array} \)
\(\begin{array}{l}=\frac{4019.2}{3}\end{array} \)
\(\begin{array}{l}=1339.73\;cm^{3}\end{array} \)


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