![]() ![]() In geometry, a cone is defined as a three-dimensional solid geometric figure having a circular base at one end and a pointed edge at the other end. A right circular cone has the axis line that passes through the center of the circular base, whereas, in an oblique cone the axis line does not pass through the center of the circular base. The two types of cones are a right circular cone and an oblique cone. The formula for the base area of a cone is A = πr 2, where r is the radius of the base of the cone. ![]() ![]() The base of the cone is the quantity that shows the area covered by the circular base of the cone. A cone with radius 'r' and height 'h' has a volume of (1/3)πr 2h. The volume of a cone is the amount of space occupied by a cone. Here, πr 2 is the area of its base, and its curved surface area is πrl. Here, 'r' is the radius of the cone and 'l' is the slant height of the cone. The formula for finding the surface area of a cone is (πr 2 + πrl) square units. The surface area of a cone can be obtained by adding the area of its base and its curved surface. The slant height is obtained by the square root of the sum of the squares of the radius and the height of the cone. The distance from the apex or top of the cone to a point on the circumference of the base is called slant height. Also in a cone, there is only one flat surface that forms the base. Since a cone has only one vertex it does not have any edge. The cone has a circular base and a curved surface. How Many Faces, Edges, and Vertices Does a Cone Have?Ī cone has one face, with no edges and one vertex. The cone has one face (which is circular) with no edges and one vertex, which is the apex of the cone. The pointed tip at the top of the cone is called 'Apex'. Volume of cone = (1/3) × volume of a cylinder.Ī cone is a three-dimensional figure which has a circular base and a curved surface. Also, the volume of a cone is one-third of the volume of a cylinder. Volume of cone = (1/3) × π × r 2 × h cubic units. Since the base of the cone is circular, we substitute the area to be πr 2. Therefore, the volume of cone= (1/3) × A × h. Let A = Area of base of the cone and h = height of the cone. The formula to find the volume of a cone, whose radius is 'r' and height is 'h' is given as, Volume = (1/3) πr 2h cubic units. The volume of a cone is the space occupied by the cone. So, whenever we are asked to calculate the surface area of the cone, it means we have to find the total surface area. Total surface area is sometimes referred to as only surface area. Total Surface Area (TSA) = Area of the base (Circle) + Curved Surface Area of the Cone(CSA). In other words, it is the sum of the curved surface area of the cone and the area of the circular base, which can be written mathematically as: Total surface area is the sum of the area of the circular base and the area of the curved part of the cone. For a cone of radius 'r', height 'h', and slant height 'l', the curved surface area is as follows:Ĭurved Surface Area = πrl square units. The curved surface area of a cone is the area enclosed by the curved part of the cone. The formula for the slant height of the cone is 'l' = \(\sqrt\) Curved Surface Area of Cone If the slant height of the cone is 'l' and the height is 'h' and the radius is 'r', then l 2 = r 2 + h 2. The slant height of a cone is obtained by finding the sum of the squares of radius and the height of the cylinder which is given by the formula given below. They are the slant height of a cone, the volume of a cone, and its surface area. There are three important formulas related to a cone. ![]()
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