A square is cut from a circle of radius r, inscribed in a circle that bounds the circle.
| November 26, 2020 | education
A square is cut from a circle of radius r, inscribed in a circle that bounds the circle. Find the area of the remainder of the circle.
Determine the area of the circle.
Scr = π * r ^ 2 cm2.
The diagonal of the inscribed square is the diameter of the circle, AC = 2 * r cm.
The diagonals of the square are equal, then BD = AC = 2 * r cm, then the area of the square is:
Skv = AC * AD / 2 = 2 * r * 2 * r / 2 = 2 * r2 cm2.
The area of the remaining figure is: S = Sokr – Skv = π * r ^ 2 – 2 * r ^ 2 = r ^ 2 * (π – 2) cm2.
Answer: The area of the remaining figure is r ^ 2 * (π – 2) cm2.
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