Question

В круге радиуса R вырезаны три круга одинакового радиуса, окружности которых касаются друг друга внешним образом, а большей окружности - внутренним образом. Определите площадь оставшейся части круга

Answer 1

Площадь круга радиуса R равна : пи*R^2 . По условию задачи вырезаны три одинаковых круга , значит их радиус равен : R/3/2 = R /6 . Площадь одного вырезанного круга равна : пи * (R/6)^2 = пи* R^2 /36  . Площадь оставшейся части круга равна : пи * (R^2 - 3 * R^2 /36) = пи* R^2(1 - 1/12) = 
11/12 * пи * R^2

Answer 2

Problem Statement

В круге радиуса R вырезаны три круга одинакового радиуса, окружности которых касаются друг друга внешним образом, а большей окружности - внутренним образом. Необходимо определить площадь оставшейся части круга.

Solution

To find the area of the remaining part of the circle, we need to subtract the combined areas of the three smaller circles from the area of the larger circle.

Let's denote the radius of the smaller circles as r. According to the problem statement, the circles are tangent to each other externally and the larger circle is tangent to the smaller circles internally.

To find the area of the remaining part, we can use the formula for the area of a circle: A = πr^2.

The area of the larger circle is given by: A_larger = πR^2, where R is the radius of the larger circle.

The combined area of the three smaller circles is given by: A_smaller = 3 * πr^2.

Therefore, the area of the remaining part of the circle is: A_remaining = A_larger - A_smaller.

Let's calculate the area of the remaining part using the given information.

Calculation

From the problem statement, we know that the radius of the larger circle is R, and the radius of the smaller circles is the same.

Let's assume the radius of the smaller circles as r.

Now, we can calculate the area of the remaining part of the circle.

The area of the larger circle is given by: A_larger = πR^2.

The combined area of the three smaller circles is given by: A_smaller = 3 * πr^2.

Therefore, the area of the remaining part of the circle is: A_remaining = A_larger - A_smaller.

Substituting the values

From the problem statement, we don't have specific values for R or r. Therefore, we can't calculate the exact area of the remaining part without knowing the values of R and r.

However, we can provide the formula and explain the process to calculate the area once the values of R and r are known.

Conclusion

In conclusion, to find the area of the remaining part of the circle, we need to subtract the combined areas of the three smaller circles from the area of the larger circle. The exact calculation requires the values of the radii of the larger and smaller circles.