What is the relationship between sector and cone?

When the sector is bent to form a cone, its radius becomes the slant height of the cone. The radius of the base of the cone is obtained from the relation r = , where r = radius of the base of the cone, R = radius of the sector, θ = angle of the sector.

How do you form a cone from a sector of a circle?

To make a cone, we start with a sector of central angle θ and radius s, we then joint points A and B letting point O move upward untill OA and OB are coincident. The radius s of the sector is equal to the slant height s of the cone.

How do you find the sector angle of a cone?

The area of the sector, and hence of the slanted surface of the cone, is therefore 2πr2πl×πl2=πrl. Alternatively, we could have worked out ϕ first, using the formula for the arc length of a sector “l=rθ”, giving in this case 2πr=lϕ, so ϕ=2πrl.

What is angle of cone?

The angle remaining in a sheet of paper after a sector has been cut out so that the paper can be rolled into a right circular cone. See also. Takeout angle.

What is angle of sector?

The angle of the sector is 360°, area of the sector, i.e. the Whole circle = πr2. When the Angle is 1°, area of sector = πr2/360° So, when the angle is θ, area of sector, OPAQ, is defined as; A = (θ/360°) × πr2. Let the angle be 45 °.

What is the net for a cone?

circle
A cone has one circular base. The net of a cone is a full circle for the base, and the a part of another circle for the wall of the cone.

How do you find the radius of an angle with a cone?

If you know the slant length s and the angle X, you can use the trig function SIN (sine) to find the radius r: r = s sin(X).

What is the angle in a cone?

the angle of the sector differs from the angle of the cone. the sector’s angle is computed using the formula θ=LR; where L is the sector’s arc length and R is the sector’s radius. now say L=Rθ.

What is central angle of a cone?

A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. The central angle is also known as the arc’s angular distance. The size of a central angle Θ is 0° < Θ < 360° or 0 < Θ < 2π (radians).

How do you find volume of a sector?

Volume of a spherical sector = (2/3)πR2h, where, R is radius of sphere, h is height.

How do you find the volume of a sector of a cylinder?

If the inner radius is set 0 and the number of degrees is 360, we will calculate the volume of the cylinder. The formula is simple – the area difference of the segments obtained by the first and the second radius, multiplied by the height.

How to find the surface area of a right circular cone?

A right circular cone is a circular cone whose axis is perpendicular to the base. Surface area of cone = πr (r+√ (h 2 +r 2 )) where r is the radius of the circular base. h is the height of the cone. Slant height of the cone, L = √ (h 2 +r 2) Therefore, Surface area = πr (r + L)

How do you find the slant height of a cone?

The slant height of a cone is calculated using the formula s=√ (r 2 + h 2) units, where “r” is the radius and “h” is the height of a cone. What is the lateral surface area of a cone? The lateral surface area of a cone is calculated using the formula, LSA =πr√ (r 2 + h 2) square units. This is all about the area of a Cone.

How do you find the angle of a cone with sector?

the sector’s angle is computed using the formula θ = L R; where L is the sector’s arc length and R is the sector’s radius. now say L = R θ. when you make a cone using the sector, its arc length will become the cone’s base perimeter. so you can write 2 π r = R θ; where r is the cone’s base radius.

How do you find the volume of a cone?

The formula for the volume, V, of a cone is the same as the volume for a pyramid, which is: where B is the area of the base and h is the height. Since the base for a cone is a circle, the base area is B=πr 2. Therefore, the volume of a cone is: where r is the radius of the base.