Right Circular Cone

What is a right circular cone?

A cone in which the centre of the circular base is perpendicular to the vertex of the cone is called the right circular cone. We can obtain a right circular con by rotating a right triangle along its perpendicular or base.

What is the relationship between the slant height, height, and radius of a right circular cone?

The relation between slant height, height and radius of the right cone is,

l2 = h2 + r2

What is the volume of a right circular cone?

The volume of the right circular cone is the total space occupied by the cone. It is calculated using the formula,

V = 1/3 × πr2 h

What is the surface area, or total surface area, of a right circular cone?

The total material required to build the cone is called the Total Surface Area of the cone. It is calculated by adding the CSA and the area of the circular base of the cone. Its formula is,

Total Surface Area of Right Circular Cone = π(r + l)r

What is the curved surface area of a right circular cone?

The area of the curved surface of the right circular cone is the Curved Surface area of the right circular cone. It is calculated using the formula,

Curved Surface Area of Right Circular Cone = πrl

What is the face of a right circular cone?

A cone has two faces:

  • One flat face, which is the base, and
  • One curved face, which is circular.

What is an example of a right circular cone?

An example of a right circular cone is an ice cream cone. It has a pointed apex, a circular base, and a curved lateral surface. Traffic cones, party hats, and volcano shapes are also examples of right circular cones.

What is the difference between the CSA of a cone and the TSA of a cone?

CSA (Curved Surface Area) of a cone refers to the area of the curved surface that wraps around the cone, excluding the base. The TSA (Total Surface Area) of a cone includes both the CSA and the area of the circular base. Mathematically, CSA = πrl, where r is the radius of the base and l is the slant height, while TSA = CSA + πr2, where r is the radius of the base.

Is a cone a 3D shape?

Yes, a cone is a three-dimensional (3D) shape. It has a circular base, a curved lateral surface, and a pointed apex. Cones belong to the category of geometric solids in three-dimensional space.

What is the SA of a right circular cone?

For a right circular cone of height ‘h’, radius ‘r’ and slant height ‘l’, the SA is:

  • Curved surface area of right circular cone = π r l
  • Total surface area of a right circular cone = π(r + l)rIs a


Right Circular Cone

A right circular cone is a 3D shape with a circular base and a curved surface that narrows to a point known as the apex or vertex. The cone’s axis is the line connecting the vertex (apex) to the centre (midpoint) of the circular base. This axis is perpendicular to the base, creating a right angle.

The volume formula for a right circular cone is V = (1/3) × πr2h, where:

  • r is the radius of the base circle cone
  • h is the height of the cone

This formula tells us that the volume of a cone is one-third of the volume of a cylinder with the same radius and height.

Table of Content

  • What is a Right Circular Cone?
  • Right Circular Cone Definition
  • Right Cone vs Oblique Cone
  • Properties of a Right Circular Cone
  • Surface Area of a Right Cone
  • Volume of a Right Circular Cone
  • Frustum of a Right Circular Cone
  • Equation of Right Circular Cone
  • Examples of Right Circular Cone

Similar Reads

What is a Right Circular Cone?

A cone whose axis is perpendicular to the plane of the base of the cone is called a right circular cone. It is a 3-D figure in which a flat circular surface meets a curved surface at the point on top of the figure. We can imagine the right circular cone as the shape drawn out from the cylinder taking its base,, but as we start to go up, the radius of the cone gets smaller until it becomes zero,, and the cone is closed at that point....

Right Circular Cone Definition

If the axis in any cone is perpendicular to the plane of the base of the cone, then the cone is called a right circular cone. We can form a right circular cone by rotating any right-angle triangle along its base or height....

Right Cone vs Oblique Cone

A cone is a 3D shape that resembles a triangular shape with a circular base. We can classify the cones into two types based on their alignment of the vertex and the centre of the circular base:...

Properties of a Right Circular Cone

A right circular cone,, or simply a right cone,, is a unique 3D shape that has various properties. Some of the important properties of the right cone are:...

Surface Area of a Right Cone

Surface area of a right circular cone is the total region occupied by the surface of the three-dimensional shape and is measured in terms of square units such as sq. cm (cm2), sq. m (m2), etc. A right circular cone has two surface areas:...

Volume of a Right Circular Cone

The total space occupied by the right circular cone is defined as the volume of the right circular cone. We can also define the volume of the right circular cone as the amount of total material that the cone contains. The volume of a cone is expressed in cubic units like m3, cm3, etc....

Frustum of a Right Circular Cone

If we cut a right circular cone by a plane parallel to its base, the figure so obtained is called the frustum of the right circular cone. There are various objects that are in the shape of the frustum of the cone. The most common object that resembles the frustum of a right circular cone is the bucketthe....

Equation of Right Circular Cone

We can represent the right circular cone in 3D space with the equation discussed below. If the vertex of the cone is at the origin and the cone is arranged in x, y, and z directions, then the equation of the cone is:...

Examples of Right Circular Cone

Below are some real-world examples of right circular cones:...

Right Circular Cone Solved Questions

Question 1: Calculate the surface area when the radius and slant height of a right cone arecones 7 inches and 13 inches, respectively. (Use π = 22/7)...

Practice Questions on Right Circular Cone

If the radius of the base of a right circular cone is 6 cm and its height is 8 cm, what is the slant height of the cone? A right circular cone has a slant height of 10 meters and a radius of 4 meters. What is the total surface area of the cone? The volume of a right circular cone is 100π cubic centimeters, and its radius is 5 centimeters. What is the height of the cone? A right circular cone has a height of 12 inches and a slant height of 15 inches. What is the radius of its base? If the volume of a right circular cone is 200 cubic units and its height is 10 units, what is the radius of its base?...

FAQs on Right Circular Cone

What is a right circular cone?...