Question

Помогите пожалуйста! Дам 50 баллов. Длина дуги окружности, на которую опирается центральный угол в 60 градусов, равна 2 см. Найдите радиус окружности с точностью до 0,01 см и площадь сектора, образованного этим углом, с точностью до 0,1 см² 6 КЛАСС МУРАВИН МУРАВИНА

Answer 1

Calculation of the Radius of the Circle

To find the radius of the circle, we can use the formula for the length of a circular arc:

Length of Arc = (θ/360) × 2πr

where θ is the central angle in degrees, r is the radius of the circle, and 2πr is the circumference of the circle.

In this case, the central angle is 60 degrees and the length of the arc is given as 2 cm. We can substitute these values into the formula and solve for r:

2 = (60/360) × 2πr

Simplifying the equation:

2 = (1/6) × 2πr

Dividing both sides by (1/6) × 2π:

r = 2 / [(1/6) × 2π]

r = 2 / (1/3π)

r = 6 / π

Using the value of π as approximately 3.14159, we can calculate the radius:

r ≈ 6 / 3.14159

r ≈ 1.90986 cm

Therefore, the radius of the circle is approximately 1.91 cm.

Calculation of the Area of the Sector

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

Area of Sector = (θ/360) × πr²

where θ is the central angle in degrees and r is the radius of the circle.

In this case, the central angle is 60 degrees and the radius is approximately 1.91 cm. We can substitute these values into the formula and calculate the area:

Area = (60/360) × π × (1.91)²

Area = (1/6) × 3.14159 × (1.91)²

Area ≈ 0.5236 × 3.641881

Area ≈ 1.90986 cm²

Therefore, the area of the sector, formed by the 60-degree central angle, is approximately 1.91 cm².

Please note that the calculations are rounded to two decimal places for simplicity and the given precision of 0.01 cm and 0.1 cm².