A three-dimensional shape in geometry that tapers from a flat base to a point is known as a cone. This common point where all the line segments connect is called the apex or the vertex. Lines starting from the apex extend up to all points on the base. Students have to learn about several concepts such as properties, volume, and surface area of cone in order to claim to be masters of the topic. We can also think of a cone as a pyramid that has a circular cross-section, except that a pyramid has a triangular cross-section. Before we can move on to learning about a cone, we need to first start by understanding certain terminologies associated with a cone.
Terms Associated with Cones
- Height: The perpendicular distance from the vertex of the cone to the base of it is known as the height.
- Radius: The distance from the center of the base to any point on its circumference is called the radius.
- Slant Height: The distance between any point on the circumference of the base to the vertex or apex of the cone is called the slant height.
Slant Height
We can calculate the slant height by using the Pythagoras theorem. Suppose l represents the slant height, h is the height, and r is the radius. These form the sides of a right triangle, with l being the hypotenuse r is the base, and h is the perpendicular. The following formula is used to find the slant height.
Slant height l = √(r2 + h2)
Surface Area
There are two types of surface areas:
- Curved Surface Area (CSA)
- Total Surface Area (TSA)
Curved Surface Area
The CSA of a cone can be defined as the area occupied by only the curved surface of that figure. Thus, it does not include the base. We can also say that the area occupied by the unfolded cone or the unrolled lateral area is called the CSA.
CSA = pi * r * l
where r is the radius, pi is a constant with values either 22/7 in fractional form or 3.14 in decimal form, and l is the slant height.
Total Surface Area
The TSA of a cone can be defined as the area occupied by the curved surface of that figure and the base. Therefore, it is the total area occupied by the cone.
TSA of a cone = CSA + base = pi * r * l + pi * r2 = pi * r (l + r)
As the area of the base is pi *r2, we add that to the CSA to get the TSA.
Volume
The volume of a cone can be defined as the capacity of the cone. The volume of cone formula can be given as follows:
Volume = ⅓ * area of the base * height = ⅓ * pi * r2 * h
We can also say that a cone’s volume is equal to one-third of a cylinder having the same measure of height and radius.
Conclusion
For understanding how to work with a cone completely, kids must also have a foundation in the volume and surface areas of other shapes. Children can join an educational platform such as Cuemath to gradually learn about all figures and the properties associated with each. The math experts focus on clearing concepts and making the lectures an enjoyable experience for the child. Thus, a kid is sure to succeed not only in his school and competitive exams but also at an industry level where he is required to solve research-level problems.
