Calculate cone area

Cone

Do you need calculate the area of a cone? Use our calculator and you will be able to do it immediately from the radius of the base and the length of the generatrix of this geometric figure.

For orbtain the area of the cone just fill in these data in the calculator and press the calculate button, but remember that both the radius and the generatrix must be in the same units for the result to be correct. If for example you have the radius in centimeters and the generatrix in meters, you must convert one of them to match.

Formula for calculating the area of a cone

Calculate cone area

To calculate the area of a cone there are two formulas that we can apply depending on whether we want to calculate the lateral area or the total area of the figure:

  • The side area is the sum of all the lateral faces of the cone and is represented by the abbreviation AL.
  • The total area is the sum of the lateral faces and the base of the figure. In this case it is represented by AT.

The formula to be used in each case is as follows:

Lateral area = π x radius x generatrix

Total area = π x radius x (generatrix + radius)

As we said at the beginning, it is imperative that the measures of the generatrix and the radius are in the same units (all in centimeters, all in meters, etc. but one can never be in centimeters and the other in meters).

How to calculate the area of a cone from its height?

If the problem data gives us the height of the cone but not the length of its generatrixit's OK. We can calculate the area of the figure anyway although we will have to apply some more formula in the process.

If you look at the representation of the cone above these lines you can see that the height, the radius and the generatrix form a right triangle, which allows us to apply the Pythagorean Theorem. Therefore we have that:

g2 = r2 + h2

We clear the unknown that will give us the value of the generatrix of the cone and we have that:

g = √(h2 +r2)

Let's look at it with a practical example. We have to calculate the area of a cone of 6 centimeters in height and 4 centimeters in diameter. The first thing to do is to calculate the length of the generatrix from the above formula:

g = √(h2 + r2) = √(36 + 4) = 6.32 centimeters

Notice that we have been given the value of the diameter of the base so we had to divide by two to get the radius.

Now we can calculate the area of the cone from the formula:

Lateral area = π x radius x generatrix = π x 2 x 6,32 = 39,69 cm2

Total area = π x radius x (generatrix + radius) = π x 2 x (2 + 6,32) = 52,25 cm2

It's easy, isn't it? If you have any questions for find the area of a cone leave us a message and we will help you as soon as possible.

If you want to calculate the volume of a cone you can click on the link we have just left and you will be able to do it.

2 thoughts on “Calcular área del cono”

  1. You know that I found it very interesting and accurate to everything in this post, although I was left with a doubt; can I calculate the basal area of a cone just by knowing the height and the generatrix?

    I am a high school student in Chile and I was asked this question in class: "Determine the basal area of a cone if its generatrix is 20 cm and its height is 16 cm" I have tried to do it but I can not find the result, if you do me the favor of solving it and explain it to me please.

    Reply
    • Hello Felipe,

      The problem you want to solve is very simple. The first thing we have to calculate is the radius of the base circle. Since you have the height and the generatrix of the cone, we will solve the missing unknown (the radius) using the Pythagorean Theorem:

      r = √(g2 - h2) = √(400 - 256) = √144 = 12cm

      Now that you know the radius of the base of the cone, we can calculate the circle area by applying the following formula:

      Basal area of the cone = πr2 = 144π = 452,39cm2

      With that you have the exercise solved.

      Greetings!

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