Surface Area of a Cone Calculator
In Geometry, some figures aren’t simple to deal with because of their complex shapes. A cone is one of those shapes that you can’t solve with simple steps. To find the area of a cone, you should have to be proficient and experienced. It is because the shape of this figure is a little complex and demands some extra attention for calculation.
If you don’t know how to do this or find it difficult, you can use the surface area of a cone calculator. This maths calculator will help you with the calculation of the total area of the cone and the area of the curved side of the cone. You can read about this online tool as well as get information about a cone here on this page in detail.
Table of Contents
Surface Area of a Cone Definition
To understand what is the surface area of a cone, you first need to learn what is a cone. It is a three-dimensional shape that spreads in all three directions length, width, and height. No doubt, multiple figures belong to the 3-D category but a cone is different from others because of its curved shape.
Unlike other shapes, a cone doesn’t spread straight but it has curved sides and a round upper or lower part. With this type of unique shape, the surface area of a cone is the total covering of the shape from top to bottom and left to right. As this figure has a different shape, so, its parameters are not the same as the other figures.
Here are some important terms that belong to a cone and are used when we are calculating different measures related to it.
- Radius: It is the distance of any corner on the curved side of the cone from its center.
- Slant Height: The length of any curve side of a cone is called its slant height.
- Slant Height: The vertical distance from the upper corner of the cone to the center of the curved part is called its height.
How to derive the surface area of a cone formula?
When it comes to the calculation of the surface area of a cone, we need to use most of the above-mentioned measures. A cone involves two different sections related to which we can find the area of a cone. One part of a cone is called it's base while the other part is called lateral.
To find the total surface area of a cone, we have to calculate areas related to these parts separately and then merge them. Here are the formulas related to these sections' area calculations and the overall surface area of a cone.
Area of base of a cone = 𝝿r2
Similarly, we can find the surface area of the lateral part of the cone using the following formula.
Lateral area of a cone = 1/2 .c . l
As this part is curved like a circle, that’s why its formula involves the circumference that is shown by “c” in the above formula. In terms of radius, we can also rewrite the above lateral area as,
Lateral area of a cone = 𝝿 . r . l
By using these formulas, we can find the total surface area of a cone. Here is the formula derivation for this calculation that we have done using the above formulas.
Surface Area of a cone = (𝝿 . r2) + (𝝿 . r . l)
We can simplify this formula as,
= 𝝿 . r . (r + l)
So, it is the total surface area of a cone that you have to use for solving questions related to it.
How to find the surface area of a cone?
Let us share an example here to let you know how to solve its related questions.
Example 1:
Find the surface area of the cone if the radius is 3 meters and the slant height is 5 m.
Solution:
To find the surface area of this cone, we only have to put the values of “r” and “l” in the above-derived formula.
Surface Area of a cone = 3.14 (3) (3 + 5) square meters
= 75.398 square meters
How to use the surface area of a cone calculator?
Using this tool by Calculator’s Bag is not difficult because you only have to input values in the concerned boxes. Here are the steps you need to follow for this calculation.
- Enter the measure of radius in the first box.
- Write the measure of slant height in the second box.
- This tool will automatically show you the final answer as the surface area of a con.
FAQ | Surface Area of a Cone Calculator
What is the rule of the surface area of the cone?
To find the surface area of the cone, you need to know the measure of its radius and slant height. You can also find it using the simple vertical height but it will be a little difficult process.
Do you need slant height for the surface area of a cone?
Yes, it is needed to make the process of calculation simpler. If you don’t have this measure, you can still find the surface area but it will be a difficult and lengthy process.
What is the difference between the lateral surface area and the base area of a cone?
The circular area of a cone is called it's base area while the side area of the same cone is called its lateral area.
What are the applications of the surface area of a cone calculator?
With the help of the surface area of a cone calculator, you can easily complete your educational assignments. Also, it can help you in professional mathematics when you have to find the measures of a design with complex values.
