Calculating the volume of a cone is very simple when you know its height, the radius of the base and the formula for calculating the volume. The mathematical formula for calculating the volume of a cone is as follows: v = hπr2/3.
Steps
Method 1 of 1: Calculate the Volume of a Cone
Step 1. Locate the radius
If you already know the radius measurement, you can go to the next step. If you know the diameter measurement, simply divide it by 2 to get the radius measurement. If, on the other hand, you know the measurement of the circumference of the base, divide it by 2π and get the measurement of the diameter. In case you do not know any of these data, get a ruler and proceed to measure the widest point of the circular base (the diameter), then divide it by 2 to obtain the measurement of the radius. Let's assume that in our case the radius measures 1.3 cm.
Step 2. Use the radius to calculate the area of the base
To calculate the area of a circle, you simply need to use the following mathematical formula: A = πr2. Replace the variable "r" with the measure of the radius obtained in the previous step, i.e. 1, 3 cm, thus obtaining A = π (1, 3)2. Now square the radius measurement and then multiply it by the "π" value. This way you will get the area of the base of your cone. A = π (1, 3)2 = 5, 3 cm2.
Step 3. Find the height of the cone
If you already know this measurement, write it down. If not, use the ruler to measure the height of your cone. Let's assume that the height of our cone is equal to 3.8 cm. Make sure the height of the cone is in the same unit as the radius.
Step 4. Multiply the area of the base by the height of the cone
Then proceed to multiply 5.3 cm2 for 3, 8 cm. You will get 5.3 cm2 x 3, 8 cm = 20, 14 cm3
Step 5. Divide the result by 3
To calculate the volume of your cone, divide the result obtained by 3, i.e. 20, 14 cm3 / 3 = 6, 7 cm3. The volume of an object is always expressed with a cubic unit of measurement, since it measures the space occupied in the three dimensions.
Advice
- Make sure your measurements are accurate.
- Do not follow this procedure until you have finished eating the ice cream in the cone.
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How does it work:
With this method, you will calculate the volume of the cone as if it were a cylinder. By calculating the base area and multiplying it by the height, you are calculating the volume of the entire base area projected over the entire height, thus obtaining the corresponding cylinder. Since a cylinder contains exactly three cones (of equal base and height), you simply divide the result by 3. This way you will have identified the volume of a single cone
- Make sure all data is expressed in the same unit of measurement.
- The radius, the height and the apothem of the cone (where the apothem is the segment that joins the vertex of the cone with any point of the base circumference) form a right triangle, since it relates them to each other according to the Theorem of Pythagoras: (height)2+ (radius)2= (apothem)2
