Spherical Sector Formula
Spherical Sector Formula
The shape of a spherical sector is similar to an ice cream cone. The spherical sector is defined mathematically as the region of the sphere that has a vertex at its centre and a conical boundary. Its zone refers to the sphere’s bottom. It might be the union and spherical crown of a cone. One can apply the Spherical Sector Formula to calculate the spherical sector’s volume and surface. A solid called a spherical sector is created by rotating a circle’s sector along an axis that runs through its centre but has no points inside the sector. The resulting sector is a spherical cone if the revolution axis is one of the radial sides; otherwise, it is an open spherical sector. A spherical sector is surrounded by a zone and one or two conical surfaces. The region of the sphere with a vertex at the centre and a conical boundary is known as a spherical sector.
The Spherical Sector Formula by Extramarks is among the best resources for students preparing for their exams. The Spherical Sector Formula provides clear and concise solutions to all of the issues required to understand the concept. The Spherical Sector Formula has been created and verified by professionals with years of expertise in high school exams. Consequently, they can be trusted because they are entirely accurate and error-free. The Spherical Sector Formula follows the requirements to help students get the best grades possible. Every aspect has been extensively discussed in order to aid students in comprehending the fundamentals to the fullest extent possible. Harder problems have been broken down into smaller parts to make them easier to comprehend. The Spherical Sector Formula properly uses diagrams to aid students in understanding the concept.
Spherical Sector Formulas
The Spherical Sector Formula has two main components that relate to the area and volume of a spherical sector. The Spherical Sector Formula for the total surface area of a spherical sector is equal to the sum of the zone’s area and the lateral areas of its enclosing cones. A spherical sector’s volume, whether open or conical, is equal to one-third of the product of the zone’s area and the sphere’s radius. A spherical sector is a region of a sphere or ball that is defined by a conical boundary with an apex in the centre of the sphere, also referred to as a spherical cone in geometry. It can be described as the combination of a spherical cap and the cone created by the sphere’s centre and base. It resembles the sector of a circle in three dimensions. A sphere’s radius describes a conical surface and divides the associated ball into two spherical sectors, one minor and the other major, while it moves along a tiny circle of the sphere, acting as a guide curve. The salient sector, or the convex of the two sectors, is commonly referred to as the spherical sector. A spherical cap and a cone, whose apex is in the centre of the sphere and whose base corresponds to the base of the spherical cap, meet in this sector.
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Sample Problems
Students need to practice several problems on the Spherical Sector Formula to completely understand the concept. Extramarks’ website offers sample problems based on the Spherical Sector Formula.
