A circle is drawn inside a square of length 4 units as shown in the fi

A circle is drawn inside a square of length 4 units as shown in the figure given above. What is the area of the shaded portion?

16-4π
16-π
4-π
4-2π
This question was previously asked in
UPSC CAPF – 2013
The figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units.
When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4/2 = 2 units.
The area of the circle is π * radius² = π * (2)² = 4π square units.
The shaded portion is the area of the square minus the area of the inscribed circle.
Area of shaded portion = Area of square – Area of circle = 16 – 4π square units.
Calculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.
The formula for the area of a square with side ‘s’ is s². The formula for the area of a circle with radius ‘r’ is πr². When a circle is inscribed in a square, the diameter (2r) equals the side (s).