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Arc, Sector and Cone

Arc

Arc is a portion of the perimeter of a circle with two endpoints. Any part of a circle's diameter is called an arc. To remember, a circle's radius is its diameter or the width across it. As a result, we can assume that the radius of a circle is the circle's entire arc.

Sector

A Sector is a portion of an area of a circle enclosed by two radii and an Arc. A sector is defined as a portion of a circle made up of the circle's arc and two radii. It's a section of the globe made up of a part of the circumference (arc) and the circle's radii at both ends.
Length of an Arc

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Where x
= Central angle of Arc.
Area of sector = πr2x/360.

Cone

Cone is a three-dimensional solid that has a circular base joined to a point by a curved side. That point is called the apex. A cone is a distinctive geometric figure with a smooth top surface and a pointed top surface. The cone's rounded end is known as the apex, while the smooth surface is known as the. Here is how a cone appears:
We can form a cone curved by a sector.
The radius of the sector, R=slant height of the cone,l.
Length of the arc of the sector = Base perimeter of the cone.
2πRx/360=2πr
Ix/360=r
Therefore, base radius of the cone,r=lx/360=Rx/360.
Central angle of the given sector =Base radius of the cone x 360/Radius of the sector.

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