Question

Four circular cardboard pieces, each of radius $7$ cm are placed in such a way that each piece touches the two other pieces. The area of the space enclosed by the four pieces is

• A. $21c{m}^2$
• B. $42c{m}^2$
• C. $84c{m}^2$
• D. $168c{m}^2$

Answer 1

Answer: (B)

$42c{m}^2$

Area of space enclosed by the circles
$=$ Area of square of side $14$ cm
$=4$(Area of quardrant of radius $7$ cm)
$=(14{)}^2-4\times \frac{1}{4}\times \frac{22}{7}\times 7\times 7$
$=196-154=42c{m}^2$
Hence, option $B$ is correct.