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