Given:
Dimeter of the circle is d.
As circle lies inside the square. So, the length of the side of square is also d units.
The area of the circle is given as,
[tex]\begin{gathered} A=\pi\times r^2 \\ r=\frac{d}{2} \\ \Rightarrow\text{ Area of circle = }\pi\times\frac{d^2}{4} \end{gathered}[/tex]
Now, the area of the square is,
[tex]\begin{gathered} \text{Area of the square = side }^2 \\ \text{Area of the square = d}^2 \end{gathered}[/tex]
To find the area of paper that wasted when the circle is cut out of the square,
[tex]\begin{gathered} A_p=\text{ Area of the square-Area of the circle} \\ =d^2-\pi\times\frac{d^2}{4} \\ =d^2-\frac{\pi(d^2)}{4} \\ =\frac{4d^2-\pi(d^2)}{4} \end{gathered}[/tex]
Answer: option D) is correct.
