如何证明圆的周长是2pir？

圆是一个封闭的二维图形，其中平面中的所有点集与一个称为“中心”的给定点等距。穿过圆的每条线形成反射对称线。除此之外，它在每个角度都围绕中心旋转对称。

圆的周长

圆的周长称为圆的周长。它是圆边界总长度的量度。它被测量为常数 π 和圆直径的乘积。例如，周长是在一个人走过圆形公园或要围起来的圆形桌子的意义上测量的。周长是一个线性值。它以长度测量单位进行测量。

圆的边界的量度称为圆的周长。圆的周长以厘米、米或公里等长度单位来衡量。

构成圆周的三个最重要的元素，

• 中心：到圆周上任何其他点的固定距离称为圆心。
• 直径：通过圆心穿过圆的距离称为直径。
• 半径：圆心到圆周上任意一点的距离。

如何证明圆的周长是 2 pi r？

回答：

The value of Pi (π) is equivalent to the ratio of the circumference of a circle to its diameter. This value is approximately equivalent to nearly 3.14159.

Mathematically,

π = C/D

where, 

C is referred to as the circumference

D is referred to as the diameter

Upon rearranging the terms we obtain, 

C = π × D

Writing in terms of radius, 

2r = D

Hence,

C = 2πr

Hence the circumference of a circle is C = 2πr

示例问题

问题 1. 求半径为3 厘米的圆的周长？使用 π = 3.14。

解决方案：

Here we have to find the circumference of the circle

Given:

Radius of the circle = 3 cm

As we know that

Circumference of the circle = 2πr

Circumference of the circle = 2 × π × r

Circumference of the circle = 2 × π × r 

Circumference of the circle = 2 × 3.14 × 3

Circumference of the circle = 18.84 cm

问题 2. 如果一个圆的直径是 36 m，求它的周长？使用 π = 3.14。

解决方案：

To find the circumference of the circle

Given: 

Diameter of the circle = 36 m

As we know that

Radius of a circle = Diameter of a circle/2

Radius of a circle = 36/2

Radius of a circle = 18 m

Now,

Circumference of the circle = 2πr

Circumference of the circle = 2 × π × r

Circumference of the circle = 2 × π × r 

Circumference of the circle = 2 × 3.14 × 18

Circumference of the circle = 113.04 m

问题 3. 假设一个圆的周长是 2200 厘米，那么求圆的半径？使用 π = 22/7

解决方案：

Here we need to find the radius of the circle when its circumference is given,

Given:

Circumference of a circle = 2200 cm

As we know that

Circumference of the circle = 2πr

2200 = 2 × π × r

2200 = 2 × 22/7 × r 

r = 2200 × 7/22 × 1/2

r = 350 cm

Therefore,

Radius of the circle is 350 cm when its circumference is 2200 cm.

问题 4. 以每米 25 卢比的速度计算半径为 30 m 的圆形游乐场的围栏成本？使用 π = 3.14。

解决方案：

Here we need to find the cost of fencing the circular playground

Given:

Radius of the circle = 30 m

As we know that

Circumference of the circle = 2πr

Circumference of the circle = 2 × π × r

Circumference of the circle = 2 × π × r 

Circumference of the circle = 2 × 3.14 × 30

Circumference of the circle = 188.4 m

Now,

Cost of fencing the circular playground =  ₹25 × circumference of the circular playground

Cost of fencing the circular playground =  ₹25 × 188.4

Cost of fencing the circular playground =  ₹4710