Question

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

• A. $168$ $c{m}^2$
• B. $158$ $c{m}^2$
• C. $148$ $c{m}^2$
• D. $138$ $c{m}^2$

Answer 1

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

Let the radius of each circle be $r.$

Then,

$4r=28cm$

$r=7cm$

Therefore,
Area of $4$ circle $=4\times \pi (7{)}^2$

$=4\times \frac{22}{7}\times 7\times 7$

$=616c{m}^2$

Area of square $={28}^2$

$=784c{m}^2$

Area of remaining cardboard $=$ Area of square $-$ Area of $4$ circles

$=784-616$

$=168c{m}^2$