- A cone is a three-dimensional (solid) figure having a circular base and a pointed edge at the top called the vertex.
- A right circular cone is similar to a regular pyramid except that its base is a circle.
- The altitude of a right circular cone is the measure of the perpendicular line segment joining the vertex and the center of the base.
- The slant height of a right circular cone is the measure of the line segment joining the vertex and any point on the circumference of the base.
- The mathematical relationship between the altitude, the radius of the base, and slant height is given by: .
- The area of the base is .
- The volume (capacity) of a cone is the amount of space occupied by it in a three-dimensional plane.
- The volume of a cone is measured in cubic units.
- If we know the radius of the base and altitude of a right circular cone, its volume can be calculated using the formula mentioned below.
where , the radius of the base, and altitude
- There are two types of surface areas associated with a right circular cone.
1. Lateral Area: It is the region occupied by the curved surface of the right circular cone.
, where the radius of the base, and slant height
2. Total Area: It is the total area occupied by a right circular cone, including the base area.
, where the area of the base
Question 1: Find the volume of a right circular cone if the radius of its base is 4 cm and its altitude is 15 cm.
Question 2: Find the lateral area of a right circular cone in terms of if the radius of its base is 3 ft and the altitude is 4 ft.
Solution: First we need to find the measure of slant height.
Question 3: Find the total surface area of a right circular cone if radius is 3 m and the slant height is15 m.
- Area of the base,
- Relation between the radius of the base, height, and slant height:
- Lateral Surface Area,
- Total Surface Area,
- The volume of the cone = volume of the cylinder.
- All the formulas mentioned in the above sections are applicable to right circular cones only.