A square metal plate with a side of 40 cm and 441 holes with a diameter of 1 cm each is used to create a drain cover. Calculate the size of the remaining square area.

The area of the square metal plate will first be calculated using the formula ${\left(side\right)}^2,$followed by the area of each circular hole, which will then be multiplied by 441 to determine the total area of the holes.

To get the area of the plate that is left, we shall finally subtract the area of 441 holes from the area of square.

Area of square metal plate $=40\times 40{ \mathrm{cm}}^2=1600{ \mathrm{cm}}^2$

Area of each hole $={\mathrm{\pi r}}^2=\frac{22}{7}\times {\left(\frac{1}{2}\right)}^2{ \mathrm{cm}}^2=\frac{11}{14}{ \mathrm{cm}}^2$

Area of 441 holes $=441\times \frac{11}{14}{ \mathrm{cm}}^2=346.5{ \mathrm{cm}}^2$

Hence, Area of the remaining square plate

 $=1600-346.5$

 $=1253.5{ \mathrm{cm}}^2$