cxercise
1. Draw a circle of li radius 5 cm () diameter 115 cm.
Answers
Answer:
Imagine a point P having a specific location; next, imagine all the possible points that are some fixed distance r from point P. A few of these points are illustrated below. If we were to draw all of the (infinite number of) points that are a distance r from P, we would end up with a circle, which is shown below as a solid line.
Thus, a circle is simply the set of all points equidistant (that is, all the same distance) from a center point (P in the example above). The distance r from the center of the circle to the circle itself is called the radius; twice the radius (2r) is called the diameter. The radius and diameter are illustrated below.
The Circumference of a Circle
As with triangles and rectangles, we can attempt to derive formulas for the area and "perimeter" of a circle. Unlike triangles, rectangles, and other such figures, the distance around the outside of the circle is called the circumference rather than the perimeter-the concept, however, is essentially the same. Calculating the circumference of a circle is not as easy as calculating the perimeter of a rectangle or triangle, however. Given an object in real life having the shape of a circle, one approach might be to wrap a string exactly once around the object and then straighten the string and measure its length. Such a process is illustrated below.
Obviously, as we increase the diameter (or radius) of a circle, the circle gets bigger, and hence, the circumference of the circle also gets bigger. We are led to think that there is therefore some relationship between the circumference and the diameter. As it turns out, if we measure the circumference and the diameter of any circle, we always find that the circumference is slightly more than three times the diameter. The two example circles below illustrate this point, where D is the diameter and C the circumference of each circle.
Again, in each case, the circumference is slightly more than three times the diameter of the circle. If we divide the circumference of any circle by its diameter, we end up with a constant number. This constant, which we label with the Greek symbol π (pi), is approximately 3.141593. The exact value of π is unknown, and it is suspected that pi is an irrational number (a non-repeating decimal, which therefore cannot be expressed as a fraction with an integer numerator and integer denominator). Let's write out the relationship mentioned above: the quotient of the circumference (C) divided by the diameter (D) is the constant number π.
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