The diameter is any straight line that connects a circle from one side to the other through its center. This measure has been known since Greek times. The first time it is dated is between 325 BC and 265 BC, coinciding with the life of Euclid of Alexandria, who is considered the father of geometry.
«A diameter of a circle is any straight line that passes through the center and ends in both directions on the circumference of the circle; this straight line also divides the circle into two equal parts.”
Another of the interesting characteristics of the diameter is that the number π (pi) is directly related to the relationship between the length of a circle and its diameter. The value of π is always close to 3.14159.
What are the uses of knowing the diameter?
Knowing the diameter is very important, for example, in careers and jobs related to Engineering, since it is essential to calculate a large number of parameters, such as the volume and weight of bodies with circular shapes, such as the cylinder or the sphere.
In hydraulics, with the hydraulic diameter, and in astronomy, with the angular diameter, they are also very important.
If what really causes you an unhealthy curiosity is to know how the area is calculated if the diameter is given, we are in luck, because it is a very simple operation that you can perform even if your knowledge of mathematics is limited or this subject is not exactly your forte in school. If you want to learn how to do it, continue reading the next post and try it for yourself. Let’s get started!
What do you need to calculate the area if the diameter is given?
You will need the following items
- A calculator
- Paper and pencil to write down the data you obtain after doing the calculation
Soon you will be able to become a master and explain to your friends how they can do this simple calculation themselves.
Instructions for calculating the area if the diameter is given
Step by step to calculate the area if the diameter is given
- To calculate the area we can do it using the following mathematical formula that we will learn to develop in this step by step: ¼ * π * diameter 2.
- We can begin this calculation by finding the square of our diameter. If, for example, our diameter is a total of, say, 7 cm, if we square it the resulting quantity will be 49 cm. 7 * 7 = 49 .
- Next, we will dedicate ourselves to finding ¼ of π to continue with the formula. If we have agreed that the number π is equal to 3.1415, we will only need to divide this amount by 4 to find out how much ¼ would be. Thus, 3.1415 / 4 = 0.875375.
- Since we have already solved the two unknowns, the only thing that remains, according to the formula that we have indicated in step 1, is to multiply ¼ of π by the squared diameter that we have already calculated. Therefore, the calculation to be carried out would be the following: 875375 * 49 = 38.483375.
- Another formula to represent the count that we have just learned is: A= π * D 2/4. You will see that the result is exactly the same. In this specific case, the order of the factors does not alter the product.
Tips for calculating area if diameter is given
Last minute tips.
It is also quite normal to learn to calculate the area of a circle with the radius, which corresponds to the distance between the center point of the circle and one of its sides, or what is the same, half the diameter.
- If you want to calculate the area from the radius, in that case the formula to solve is the following: A = π * r 2. Let’s see how it’s done.
- In this case we would have to raise the radius to the square. We know that the radius corresponds to half the diameter, therefore, if the diameter is 7, the radius will be 3.5.
- We would find the square by multiplying the diameter divided by 2 and raised to the square, (D /2)2. The result would be 12.25. If we solve this formula, it would be the same as the diameter squared divided by 4, D 2 /4, which would give us the 7 that correspond to the diameter multiplied by itself, which would be a total of 49, and divided by 4, giving a total of 12.25.
- Now we only need to multiply the diameter by π and we will have found the area. 12.25 * 3.1415 = 38.483375.
Now that you know all the possibilities, you only need to use the one with which you feel most comfortable.