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Right‌ Circular‌ Cone

Right‌ ‌Circular‌ ‌Cone

A right circular cone has an axis that is perpendicular to the plane of the base. A right circular cone is one whose altitude or height is perpendicular to the radius of the circle. The point produced at the end of the cone is known as the apex or vertex, and the flat surface is known as the base.

Cones are commonly right circular in elementary geometry, where circular implies the axis passes from the circular base creating a 90-degree right angle.

A right circular cone is a cone with a circular base and an apex immediately above the base's centre.

What is the relationship between a cone's R and L?

A cone's slant height is denoted by the letter 'l.' The letter 'h' represents the height of a cone. The radius of a cone's base is denoted by the letter 'r.'

We may utilize the Pythagorean theorem to discover a relationship between l,h, and r since height is perpendicular to the base of a cone.

What is the mathematical formula for a right circular cone?

We have for a right circular cone with radius 'r,' height 'h,' and slant height 'l'.

Curved surface area = πrl.

The total surface area = πr(l+r).

Volume = 1/3r²h.

A cone's radius is the radius of its circular base. A cone's radius may be calculated using its volume and height.

The volume of the right circular cone is one-third of the product of the area and height of the circular base.

What is the formula for calculating the radius of a right circular cone?

A radius is the distance between the centre of a circle and any point on its perimeter, also known as its circumference. A cone's radius is equal to the radius of its circular base. A radius may be calculated using its volume and height. Multiply the volume by three.

Which is the longer of the two for a right circular cone?

A right circular cone's slant height is always greater than the cone's height.

Which of the following is referred to as the cone's axis?

The cone's axis is the segment whose ends are the vertex and the base's centre. The cone is a right cone if the axis is perpendicular to the plane of the circle; otherwise, it is an oblique cone.

What is the difference between a cone's height and slant height?

A cone has three dimensions: length, width, and height. The vertical height (or altitude) is the perpendicular distance between the top and the bottom. The slant height is the distance from the top of the structure down the side to a point on the base circle.

Calculate the curved surface area, total surface area, and volume of the right circular cone if the radius is 2 cm, height is 6 cm, and length of the cone is 14 cm.

Given: r = 2 cm, h = 6 cm, l = 14 cm.

Curved surface area = πrl = * 2 * 14 = 87.96 cm².

The total surface area = πr(l+r) = * 2 (14 +2) = 100.53 cm²

Volume = 1/3πr²h = 1/3π * 2 * 2 * 6 = 25.13 cm³

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