The volume of a cone can be defined as the space or the capacity that is being held by the cone. Now, this turns up to a preliminary discussion – What is a cone?
A cone is a geometrical structure that has circular bases. The structure starts from a flat base to an apex at the top. You can create a cone by drawing lines or line segments from a flat base.
In another way, you can spot a cone by identifying it as a set of non-congruent circular disks which are placed on top of one another. The figure is structured in a manner that the ratio of the disks which are placed on top of each other remains the same.
After knowing the structure and volume of the cone, let us know about the formula of the volume of a cone.
The formula of Volume of a Cone
As already discussed, a cone is a pyramid-like structure with the base having a circular cross-section. A right cone is a pyramid structure that has its vertex over the center point of its base. This structure is also known as the right circular cone.
The formula of volume of a cone is an important part of the chapter. In the examination, students are examined on basis of their knowledge of this formula. The formula is pretty simple if you know the measurement of the height and radius of the cone.
So, the formula of the volume of a cone is = (1/3) πr2h cubic units.
In this formula,
- ‘r’ is the radius of the base of the cone.
- ‘l’ is the slanting height measurement of the cone.
- ‘h’ denotes the height of the cone.
An interesting fact: In the formula, did you notice the volume of the cone is one-third of the volume of the cylinder? So, we can say that if we take the ⅓ capacity of the cylinder, we have the capacity or volume of the cone!
Please Note: Students must know the formula for the volume of the regular cone will be equal to the formula for the right circular or oblique cone.
The volume of Cone With Only Height and Radius
If in the question, you are provided with only the height and radius of the cone, you need to apply the following formula to estimate the volume of the cone:
V = (1/3)πr2h cubic units
The Volume of Cone With Only Height and Diameter
Now, if you are provided with only the height and diameter of the cone, use the following formula to find out the volume of the cone:
V = (1/12)πd2h cubic units
Volume of Cone With Only Slant Height
Suppose, you are provided with only the measurement of the slanting height of the cone, then you can estimate the volume of the cone by applying the Pythagoras Theorem.
We know, h2 + r2 = L2
Here the h is the height of the cone, r is the radius, and l is the slant height of the cone.
What is the Surface Area of Cone?
The surface area of the cone can be defined as the total area which is being covered by the surface of the cone. The total surface area of the cone means the area which is covered by the base area and the lateral surface area of the cone.
The base area of the cone means the circular base area while the lateral surface area of the curved surface area of the cone. The circular base area can be calculated by using the formula of the area of the circle, and the lateral surface area can be calculated by estimating the side area of the cone. Visit Cuemath for much enhanced mathematical concepts.
What is the Formula of the Surface Area of the Cone?
The surface area of the cone is the total area being covered by the three-dimensional figure of the cone. As discussed, the total surface area of the cone will be the sum of the curved surface area and the circular base area of the cone.
The formula is as follows – πr(r+√(h2+r2))
Here r is the radius of the circular base, h is the height of the cone,
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