A rectangle with the largest area is cut out of a circle with a radius 5 units. What is the area of the remaining portion?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 25(π - 2).
Area of the circle = πr2
Area of the circle = 25π
According to the question,
The largest rectangle that can be cut from a circle is the inscribed rectangle, which is a square in this case.
The diagonal of the square is equal to the diameter of the circle, diameter = 2 × 5 = 10 cm
⇒ Side of the square = a = d/√2
⇒ a = 10/√2 = 5√2
Area of the square = a2 = (5√2)2 = 25 × 2 = 50
Area of the Remaining Portion = Area of circle - Area of square
⇒ 25π - 50
⇒ 25(π - 2)