Math, asked by nancypari19, 3 months ago

PRACT
een lege relation between radius, ameter and circunference of a circle.
verzas me miestera lengas (11 m. 22 33 ) etc. thread and ruler
Mease telenone the pieces of wire sing a ruler.
Fezes feine for the remaining pieces of wire​

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Answers

Answered by Shilowallace6
1

Every circle has a center, which is a point that lies exactly at the... well... center of the circle. A circle is a shape where distance from the center to the edge of the circle is always the same:

Circumference of a circle

The circumference is the distance around a circle (its perimeter!):

Here are two circles with their circumference and diameter labeled:

Let's look at the ratio of the circumference to diameter of each circle:

Circle 1 Circle 2

\dfrac{\text{Circumference}}{\text{Diameter}}  

Diameter

Circumference

​  

start fraction, start text, C, i, r, c, u, m, f, e, r, e, n, c, e, end text, divided by, start text, D, i, a, m, e, t, e, r, end text, end fraction: \dfrac{3.14159...}{1} = \redD{3.14159...}  

1

3.14159...

​  

=3.14159...start fraction, 3, point, 14159, point, point, point, divided by, 1, end fraction, equals, start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39 \dfrac{6.28318...}{2} = \redD{3.14159...}  

2

6.28318...

​  

=3.14159...start fraction, 6, point, 28318, point, point, point, divided by, 2, end fraction, equals, start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39

Fascinating! The ratio of the circumference CCC to diameter ddd of both circles is \redD{3.14159...}3.14159...start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39

\dfrac{C}{d} = \redD{3.14159...}  

d

C

​  

=3.14159...start fraction, C, divided by, d, end fraction, equals, start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39

This turns out to be true for all circles, which makes the number \redD{3.14159...}3.14159...start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39 one of the most important numbers in all of math! We call the number pi (pronounced like the dessert!) and give it its own symbol \redD\piπstart color #e84d39, pi, end color #e84d39.

\dfrac{C}{d} = \redD{\pi}  

d

C

​  

=πstart fraction, C, divided by, d, end fraction, equals, start color #e84d39, pi, end color #e84d39

Multiplying both sides of the formula by ddd gives us

C = \redD\pi dC=πdC, equals, start color #e84d39, pi, end color #e84d39, d

which lets us find the circumference CCC of any circle as long as we know the diameter ddd.

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