Calculate the volume of a cone is quite easy as long as we remember the formula to apply, unfortunately, this does not always happen so for these cases we have created an online calculator that will find the volume of the cone from its height and the radius of the base. Enter both data in the tool below, press the calculate button and you will get the volume of the figure.
In the event that we are given the length of the generatrix (g), we can calculate the height (h) or the radius (r) from the Pythagorean Theorem (it is a right triangle as you can see in the picture). Then we write the results in the calculator and that's it. If you want to calculate the cone areaClick on the link we have just left and you will be able to do it.
How to calculate the volume of a cone
To manually calculate the volume of a cone we have to square the value of the radius, multiply the result by the height and by the number PI. When we have done these three multiplications, it is necessary to divide the quantity by three to obtain the final volume. This is summarized as the following mathematical formula:
As you can see, this is a very simple but difficult to remember formula and if we don't calculate volumes regularly, we forget these kinds of things. Fortunately, we don't want you to depend on formulas, so we offer you a calculator that does all the operations for you.
Exercises to calculate the volume of a cone
As a practical example of the theory seen in the previous point, let's imagine that we have a cone with height of 12 centimeters and whose base has a diameter of 6 centimeters.s.
We apply the formula to obtain the volume of a cone and we have that:
V = (π x 32 x 12) / 3 = 113.094 cm (113.094 inches)3
Notice that in the statement of the exercise to calculate the volume of the cone we are given the diameter of the base and not the radius which is the value we need. So we divide the diameter by two and we square it.
Example with cone generatrix
Let's look at another example in which we are asked for calculate the volume of a cone from its generatrix which measures 8 cm and the radius of the base which measures 3 centimeters.
In this case, the first thing we have to do is to find the value of the height of the cone (h) from its generatrix (g) and the radius (r) of the base. To do this, we make use of the Pythagorean theorem which tells us that:
g2 = r2 + h2
We clear the unknown that will give us the value of the height and we have that:
h = √(g2 - r2) = √(64 - 9) = 7,416 centímetros.
Now that we have the height of the cone, we can apply the formula to calculate its volume:
V = (π x 9 x 7,416) / 3 = 69,892 cm3
If you have any doubts about cow to calculate the volume of this figure, leave us a comment and we will help you as soon as possible.