Diameter is the segment connecting two arbitrary points on the circle and passing through its center. Therefore, if the diameter you need to find by knowing the radius of the given circle, multiply the numerical value of the radius by two, and measure the value found in the same units as the radius. Example: the Radius of a circle 4 centimeters. To find the diameter of this circle. Solution: the Diameter is 4 cm*2=8 cm Answer: 8 inches.
If the diameter of the need to find through the length of the circle, then we must act using the first step. There is a formula to calculate the length of a circle: l=2PR, where l is the length of the circumference, 2 is a constant, n is the number equal to 3.14; R is the radius of the circle. Knowing that the diameter is double the radius, the above formula can be written as: l=пD, where D is the diameter.
To Express this formula diameter of circle: D=l/n, And substitute into it the known values, calculate a linear equation with one unknown. Example: to Find the diameter of a circleif its length is 3 meters. Solution: the diameter is equal to 3/3 = 1 m. Answer: the diameter equal to one meter.
In the mathematical tasks are often permitted to use the PI as just 3, and 3.14.
Advice 2: How to find a circle, knowing the diameter
A circle is a plane figure whose points are equidistant from its center and diameter of a circle is the line segment passing through the center and connecting two most distant points of the circumference. It diameter often becomes the variable that allows to solve most of the tasks in the geometry to find the circle.
For example, to find the circumference, sufficient to determine the source of the data is known to diameter. Ask that you are aware of the diameter of the circle is equal to N, and draw in accordance with these data, a circle. Since the diameter connects two points of circle and passes through the centre, thus the radius of the circle will always be equal to the value of half the diametera, that is r = N/2.
Use to find the length or any other value of the mathematical constant π. It represents the ratio of the circumference to the length of the diameterand the circle and geometric calculations is equal to π ≈ 3,14.
To determine the circumference, take the standard formula L = π*D and substitute the value of diameterand D = N. the result is the diametermultiplied by the factor 3.14, shows the approximate circumference.
In the case when you need to determine not only the circumference but also its area, use the value of the constant π. Only this time use a different formula, according to which the area of a circle is defined as the length of it's radius squared, and multiplied by the number π. Accordingly, the formula is as follows: S = π*(r^2).
As in the original data determined that the radius r = N/2 hence the formula for the area of a circle is modified: S = π*(r^2) = π*((N/2)^2). As a result, if you substitute in the formula the value of a known diameterand you get the desired area.
Don't forget to check what units of measurement you need to determine the length or area of a circle. If the original data determined that the diameter is measured in millimeters, the area of the circle must also be measured in millimeters. For other units cm2 or m2 the calculations are made similarly.
Advice 3: As at the circumference to determine the diameter
The circumference and diameter are related geometrical quantities. This means that the first of them can be translated into the second without any additional data. The mathematical constant, through which they are linked, is the number π.
If a circle is presented in the form of an image on paper, and its diameter is required to determine approximately measure it directly. If its center is shown in the drawing, swipe through his line. If the center is not shown, locate it with the help of a compass. To do this, use a square with angles of 90 and 45 degrees. Attach it to a 90-degree angle to the circle so that it touched both sides, and circle. Then attach the resulting straight corner 45-degree angle of a square, draw a bisector. It passes through the center of the circle. Similarly, draw in the other place the second circle on the right angle and its bisector. They intersect in the center. This will allow you to measure the diameter.
To measure the diameter, it is preferable to use a ruler made from a thin sheet of material, or tailoring meter. If you only have the large ruler measure the diameter of a circle with a compass, then without changing the solution, transfer it to graph paper.
In the absence in terms of the problem numeric data and the presence only of the drawing, you can measure the circumference using the odometer and the diameter then calculate. To use the odometer, first rotate the wheel select the arrow exactly on the zero division. Then mark on the circle point and press the odometer to the sheet so that a bar over a wheel indicated at this point. Slide the wheel along the line of the circle until the bar again will be over by this point. Read the testimony. They are in centimetres - if necessary, convert them to millimeters.
The circumference (indicated in the problem or measured by the odometer), divide it by twice the number π. Get the diameter expressed in the same units of measurement as the original data. If required by the conditions, put the calculation result into more convenient units.