Question

длина дуги окружности радиуса 10 см равна 4 пи см найдите площадь соответствующего кругового сектора

Answer 1

Если R - радиус окружности, α - градусная мера дуги, то длина дуги:
l = πR·α / 180°
4π = π·10·α / 180°
720 = 10α
α = 72°

Площадь соответствующего сектора:
S = πR² · α / 360° = π·100·72° / 360° = 20π см²

Answer 2

Calculation of the Length of the Arc

To find the length of the arc of a circle with a radius of 10 cm, which is equal to 4π cm, we can use the formula:

L = 2πr * (θ/360)

Where: - L is the length of the arc - r is the radius of the circle - θ is the central angle of the sector

In this case, the length of the arc is given as 4π cm, so we can substitute the values into the formula:

4π = 2π * 10 * (θ/360)

Simplifying the equation, we can cancel out the common factor of 2π:

2 = 10 * (θ/360)

Now, we can solve for θ:

θ/360 = 2/10

Cross-multiplying, we get:

θ = (2/10) * 360

Simplifying further:

θ = 72 degrees

Therefore, the central angle of the sector is 72 degrees.

Calculation of the Area of the Circular Sector

To find the area of the circular sector, we can use the formula:

A = (θ/360) * π * r^2

Substituting the values we have:

A = (72/360) * π * 10^2

Simplifying:

A = (1/5) * π * 100

A = 20π cm^2

Therefore, the area of the corresponding circular sector is 20π cm^2.

Please note that the calculations provided are based on the information given in the question and may vary depending on the context or specific requirements.