Understanding the Spherical Sector Formula
Picture an ice cream cone - that's a perfect everyday representation of a spherical sector. In mathematical terms, it's a part of a sphere that has its vertex at the center and a conical boundary. The base of the sphere is referred to as its zone, which can be either a spherical cap or a union of a cone. In this post, we will explore the formula to calculate the volume and surface of a spherical sector.
Here's the formula:
\[\large A=\pi r(2h+a)\]
\[\large V=\frac{2\pi r^{2}h}{3}\]
Example Problem
Question: What is the volume of a sector of a sphere with a radius of 6 cms and a cap height of 8 cms?
Solution:
Given,
r
= 6 cm
h
= 8 cm
Using the formula: