Question

Круг, радіус розміром 80 см, поділили на рівні сектори. На скільки секторів підлений круг, якщо площа кожного з них 160п см2?срочно

Answer 1

Ответ:

Круг поделен на 40 секторов ранвой величины.

Пошаговое объяснение:

Площадь круга равна пr²=п*80*80=6400п см²

Найдем ,какую часть площади составляет заданный сектор

160п:6400п= 1/40 целого круга.

Весь круг 360°

1/40*360°=9°   - это центральный угол нашего сектора. Если сектор составляет 1/40 круга,значит надо поделить на 40 равных секторов.

Answer 2

I will answer in detail. A circle with a radius of 80 cm was divided into equal sectors. How many sectors is the circle divided into, if the area of each of them is 160π cm2? Urgently.

To solve this problem, we need to use the formula for the area of a circle and the formula for the area of a sector. The area of a circle is given by the formula:

$$S = \pi R^2$$

where $S$ is the area, $\pi$ is a constant number (approximately 3.14), and $R$ is the radius of the circle.

The area of a sector is given by the formula:

$$S = \frac{\alpha}{360} \pi R^2$$

where $S$ is the area, $\alpha$ is the central angle of the sector in degrees, and $R$ is the radius of the circle.

Since the circle is divided into equal sectors, the area of each sector is the same. Let $n$ be the number of sectors. Then, the central angle of each sector is $\frac{360}{n}$ degrees. Using the formula for the area of a sector, we get:

$$160 \pi = \frac{\frac{360}{n}}{360} \pi 80^2$$

Simplifying, we get:

$$n = \frac{360 \cdot 80^2}{160 \cdot 360} = 40$$

Therefore, the circle is divided into 40 sectors.