The diagram shows a circle inside a square of side 12 cm - OCR - GCSE Maths - Question 27 - 2023 - Paper 1

The radius of the circle is half of the side of the square: $r = \frac{12}{2} = 6 \, cm$ The area of a circle is given by the formula: $A_{circle} = \pi r^2$ Substituting the value of the radius, we get: $A_{circle} = \pi (6)^2 = 36\pi \, cm^2$ This approximates to: $A_{circle} \approx 113.097 \, cm^2$

The shaded area is the area of the square minus the area of the circle: $A_{shaded} = A_{square} - A_{circle} = 144 - 36\pi$ Approximating this gives: $A_{shaded} \approx 144 - 113.097 \approx 30.903 \, cm^2$

The percentage of the shaded area relative to the area of the square is given by: $Percentage = \left( \frac{A_{shaded}}{A_{square}} \right) \times 100$ Substituting the areas, we get: $Percentage \approx \left( \frac{30.903}{144} \right) \times 100 \approx 21.48\%$