Spherical Sector Formula and Solved Example

Last Updated on Jul 31, 2023
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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:

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Frequently Asked Questions

A spherical sector is the part of the sphere with vertex at the center and conical boundary. The base of the sphere is called it’s zone.

The formula for the surface of a spherical sector is A=πr(2h+a).

The formula for the volume of a spherical sector is V=2πr²h/3.

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