Question

The following figure shows a square cardboard $ABCD$ of side $28cm$. Four identical circles of largest possible size arc cut from this card as shown below.
Find the area of the remaining card-board.

• A. $168c{m}^2$
• B. $128c{m}^2$
• C. $108c{m}^2$
• D. $129c{m}^2$

Answer 1

The correct option is A $168c{m}^2$

According to the figure,
Radius of the each circle=$7cm$
Area of one circle=$\pi (7{)}^2$
Therefore,
Area of $4$ circle=$4\pi (7{)}^2$
=$4\times \frac{22}{7}\times 7\times 7$
=$616$
Area of square=${28}^2$
=$784$
Therefore,
Remaining area=$(28{)}^2-4\pi (7{)}^2$
=$784-616$
=$168c{m}^2$