Question

ВЫЧИСЛИТЕ ДЛИНУ ДУГИ ОКРУЖНОСТИ С РАДИУСОМ 4 СМ, ЕСЛИ ЕЕ ГРАДУСНАЯ МЕРА РАВНА 120 ГРАДУСОВ. ЧЕМУ РАВНА ПЛОЩАДЬ СООТВЕТСТВУЮЩЕГО ДАННОЙ ДУГЕ КРУГОВОГО СЕ

Answer 1

Длина дуги L = πRα / 180 = π*4*120 / 180 = 8,38 см.
Площадь кругового сектора S = πR²α / 360 =π*16*120 / 360 = 16,76 см².

Answer 2

Calculating the Length of an Arc

To calculate the length of an arc on a circle, you can use the formula:

Length of Arc = (Degree Measure / 360) * 2 * π * Radius

Given that the radius is 4 cm and the degree measure is 120 degrees, we can substitute these values into the formula to find the length of the arc.

Length of Arc = (120 / 360) * 2 * π * 4

Now, let's calculate the length of the arc.

Length of Arc = (1/3) * 2 * π * 4

Using the value of π as approximately 3.14, we can simplify the equation further.

Length of Arc ≈ (1/3) * 2 * 3.14 * 4

Length of Arc ≈ (2/3) * 3.14 * 4

Length of Arc ≈ (8/3) * 3.14

Length of Arc ≈ 8.38 cm

Therefore, the length of the arc with a radius of 4 cm and a degree measure of 120 degrees is approximately 8.38 cm.