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# Right Circular Cones

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 Sub Topics A line is used to join the vertex to the midpoint of a circular base is known as right circular cone. Right circular Cones are three dimensional surfaces having circular base and only one vertex or a right circular cone having flat base, one side of a right circular cone is curved surface. It is not a polyhedral because it is having curved surface. It is a right circular cone. Where ‘h’ denotes the height of a right circular cone and ‘r’ denotes the radius of the base and‘s’ is the slant height of a right circular cone. If we want to find the volume of a right circular cone then we use the formula: Volume of a right circular cone = 1/3 ⊼r2h, Where ‘r’ is the radius and ‘h’ is the height of a right circular cone and the value of ‘⊼’ is 3.14. Some formulas related to the right circular cone are given: When we want to find the surface area of base then we use formula: Surface area of base = ⊼ * r2, Surface area of side = ⊼ * r * s, Or Surface area of side = ⊼ * r * √ (r2 + h2), Volume of a cone = ⊼ * r2 * (h / 3), ‘H’ is the height of a cone. ‘R’ is the radius of a cone. ‘S’ is the side length. The flat part is known as base of a right circular cone. Its shape is like cone. If we rotate a triangle then a new shape is formed is also called cone and a triangle is said to be a right angled triangle and it can be rotated along the shortest side. Now we see what are the properties of a cone? Now total surface area of a right circular cone is: TA = SA + ⊼r2, Where ‘r’ denotes the radius the cone’s base and ‘SA’ is the cone’s face surface area.

## TSA of Right Circular Cones

A cone is Solid shape body which has a round shape in his bottom and had a triangle type of shape as its top. The total surface area of right circular Cones can be found out with the help of simple formula, but for that we need to have basic knowledge of parameters of the cone. If we talk about cone it consists of radius, height and slant height. Radius and height are well known term to you but the slant height is a new term for you. As we well know that the volume of the cone is 1/3 πr2h, here ‘π’ is the constant whose value is 22/7 and the value will be constant whatever the condition will be, now moving to total surface area of the cone, for getting the surface area we need two things, area of the given cone and area of the base. For finding the area of the cone we need to have knowledge about the formula given below,
Area of the cone = πrl,
Here ‘π’ is the constant, ‘r’ is the radius of the cone and ‘l’ is the slant height. For finding the value of ‘l’ we need to have good knowledge about the Pythagorean Theorem. In Pythagorean Theorem the Square of hypogenous is equal to the sum of square of base and square of perpendicular. So the value of ‘l’ by Pythagorean Theorem will be √r2 + h2. Here ‘r’ is the radius and h is the height. The area of the base will be the area of circumference that will be equal to 2πr. And the total surface area will be the sum of both, so total surface area will be πrl + 2πr. We can also take ‘πr’ as common so the formula will be 2π (l + r).

## Volume of Right Circular Cones

A Right Circular Cone is a type of cone in which the axis of a right circular cone joins the vertex to the midpoint of a circular base. The volume of a right circular cone is calculated by using the following formula:
The volume of right circular cone = 1/3 ⊼ r2h,
Where, ‘r’ is the radius of a right circular cone,
‘H’ is the height of a right circular cone,

Now some of the steps for finding the volume right circular cone are;
Step1: First find the radius of a right circular cone.

Step2: After that find the height of a right circular cone.

Step 3: Volume of right circular cone is found by using radius and height of a right circular cone.

Step 4: By putting all the values of a right circular cone we get the volume of a right circular cone.

Let us assume that the radius of right circular cone is 18 inch and the height of a right circular cone is 26 inch then, what is the volume of right circular cone.
The volume of right circular cone = 1/3 ⊼ r2h.
In the first Step we see the radius of a right circular cone.
Given, the radius of Right Circular Cylinder is 18 inch.
In Step 2 we find the height of a right circular cone.
Here height is 26 inch.
The volume of right circular cone = 1/3 ⊼ r2h.
The volume of right circular cone = 1/3 ⊼ * (18)2 * 26,
The volume of right circular cone = 1/3 ⊼ * 324 * 26,
The volume of right circular cone = 1/3 ⊼ * 8424,

We know that the value of ‘⊼’ is 3.14,
Put the value of ⊼ in the formula:
The volume of right circular cone = 1/3 * 3.14 * 8424,
The volume of right circular cone = 1/3 * 26451.36,
The volume of right circular cone = 8817.12 inch3.
So the volume of right circular cone is 8817.12 inch3.

## LSA of Right Circular Cones

The axis of a Right Circular Cone joining the vertex to the midpoint of a circular base is known as a right circular cone. The lateral area of a right circular cone is calculated by using the following formula:
The lateral surface area of a right circular cone = ⊼r√ (r2 + h2),
Where, ‘r’ denotes the radius of a right circular cone,
‘H’ denotes the height of a right circular cone,
Now some of the steps for finding the lateral surface area of a right circular cone?

The steps are as follows:
Step 1: First find the radius of a right circular cone.
Step 2: After than find the height of a right circular cone.
Step 3: Now on squaring radius and height of values of a right circular cone.
Step 4: After squaring we multiply these values into another radius value.
Step 5: By putting all the values of a right circular cone we get the lateral surface area of a right circular cone.

Let’s consider the radius of right circular cone is 17 inch and the height of a right circular cone is 23 inch then, what is the lateral surface area of a right circular cone.
The lateral surface area of a right circular cone= ⊼r√ (r2 + h2),
In first Step we see the radius of a right circular cone.
Given, the radius of Right Circular Cylinder is 17 inch.
In the Step 2 we find the height of a right circular cone.
Here height is 23 inch.
The lateral surface area of a right circular cone= ⊼r√ (r2 + h2),
The lateral surface area of a right circular cone= ⊼ * 17√ [(17)2 + (23)2],
The lateral surface area of a right circular cone= ⊼ * 17√ [(289) + (529)],
The lateral surface area of a right circular cone= ⊼ * 17√ (818),
The lateral surface area of a right circular cone= ⊼ * 17 * 28.60,
Now we know the value of ‘⊼’ is 3.14.
Put in the given formula:
The lateral surface area of a right circular cone= 3.14 * 486.2,
The lateral surface area of a right circular cone= 1526.66 inch2
So the lateral surface area of a right circular cone is 1526.66 inch2.