Question

Дуга окружности соответствующая центральному углу в 240° равна 16м найдите радиус окружности

Answer 1

240градусов -16 м
360градусов  - х м
х= 360*16 :240
х=24м - длина окружности
C=2piR 
R=C/2pi=24/2*3,14=24/6,28=3,82м

Answer 2

Calculation of the Radius of a Circle

To find the radius of a circle corresponding to a central angle of 240° and a length of the arc equal to 16m, we can use the formula for the circumference of a circle.

The formula for the circumference of a circle is given by:

C = 2πr

where C is the circumference and r is the radius of the circle.

We can rearrange the formula to solve for the radius:

r = C / (2π)

In this case, the length of the arc is given as 16m. The central angle is 240°, which is equal to 2/3 of a full circle (360°). Therefore, the length of the arc is also equal to 2/3 of the circumference of the circle.

Let's substitute the values into the formula:

r = (2/3) * C / (2π)

Since the length of the arc is 16m, we can write:

16 = (2/3) * C

Now, we can solve for the circumference:

C = (3/2) * 16 = 24

Substituting the value of C back into the formula for the radius:

r = 24 / (2π) = 12 / π

Therefore, the radius of the circle is 12 / π.

Please note that the value of π is approximately 3.14159.