Question

Four circular cardboard pieces of radii $7cm$ are placed on a paper in such a way that each piece touches other two pieces. The area of the region enclosed between these pieces is

• A. $42$ $c{m}^2$
• B. $21$ $c{m}^2$
• C. $84$ $c{m}^2$
• D. $96$ $c{m}^2$

Answer 1

The correct option is A $42$ $c{m}^2$

The diameter of circle =$2\times 7=14$ cm

The circles together formed a shape square diameter of 2 circle to get from a side =$2\times 14=28$ cm

Then area of square =$a^2=(28{)}^2=784c{m}^2$

And area of each circle =$\pi r^2=\frac{22}{7}\times (7{)}^2=154c{m}^2$

So area of four circles =$4\times 154=616c{m}^2$

Then area of region enclosed between these pieces $=784-616=168$ sq cm

Then area of region enclosed between one pieces=$\frac{168}{4}=42c{m}^2$