Question

from each corner of a square of side 4 cm , a quadrant of a circle of radius 1cm is cut and also a circle of diameter 2 cm is .find the area of the remaining portion of the square?

Answer 1

$\textbf{Given:}$

$\textsf{From each corner of a square of side 4 cm ,a quadrant of a circle}$

$\textsf{of radius 1cm is cut and also a circle of diameter 2cm}$

$\textbf{To find:}$

$\textsf{Area of the remaining portion of the square}$

$\textbf{Solution:}$

$\underline{\textsf{Area of a quadrant}}$

$\mathsf{=\dfrac{\pi\,r^2}{4}}$

$\mathsf{=\dfrac{\pi\,(1)^2}{4}}$

$\mathsf{=\dfrac{\pi}{4}\;cm^2}$

$\underline{\textsf{Area of the circle}}$

$\mathsf{=\pi\,r^2}$

$\mathsf{=\pi\,(1)^2}$

$\mathsf{=\pi\;cm^2}$

$\underline{\textsf{Area of the square}}$

$\mathsf{=side{\times}side}$

$\mathsf{=4{\times}4}$

$\mathsf{=16\;cm^2}$

$\therefore\underline{\textsf{Area of the remaining portion of the square}}$

$\mathsf{=Area\;of\;the\;square-(4{\times}Area\;of\;a\;quadrant+Area\;of\;the\;circle)}$

$\mathsf{=16-\left(4{\times}\dfrac{\pi}{4}+\pi\right)}$

$\mathsf{=16-(\pi+\pi)}$

$\mathsf{=16-2\pi}$

$\mathsf{=16-2{\times}\dfrac{22}{7}}$

$\mathsf{=16-\dfrac{44}{7}}$

$\mathsf{=\dfrac{112-44}{7}}$

$\mathsf{=\dfrac{68}{7}}$

$\mathsf{=9.714\;cm^2}$

$\textbf{Answer:}$

$\mathsf{Area\;of\;the\;remaining\;portion\;of\;the\;square\;is\;9.714\;cm^2}$

Answer 2

1.answer is 68/7cm square.