Question

The wire is bent into a square of area 196 cm². The wire is rebent into a circle. Find the area, perimeter, radius, diameter of the circle​

Answer 1

$\star \: \large \underline{{ \underline{\red{ \sf \: given : }}}}$

• Area of Square = 196cm²

$\large \frak{here ..}$

☆ Area of square = area of circle

$\\ \large \purple{ \rm \:as \: \: wire \: \: of \: \: same \: \: perimeter \: \: is } \\ \large \purple{ \rm \: rebent \: \: to \: \: form \: \: circle.}$

• Finding Perimeter of square :

$\\ \large \mapsto \: \blue{ \boxed{ \green{ \sf \: area =sid {e}^{2} }}}$

$\large \sf : \implies \: 196 {cm}^{2} = sid {e}^{2} \\ \\ \large \sf : \implies \: \sqrt{196 {cm}^{2} }= sid {e}^{} \\ \\ \large \sf \therefore \: side = 14cm$

$\large \pink{ \boxed{ \orange{\sf \: perimeter = 4 \times side}}}$

$\large \sf : \implies {perimeter = 4 \times 14cm} \\ \\ \large \sf \therefore \: \green{perimeter = 56cm}$

Since, Length of wire = Perimeter of square

So,

• Perimeter of square = Circumference of circle

$\\ \large \leadsto \boxed{\pink{ \sf \: circumfrence = 2\pi r}}$

$\\ \large \sf \implies \: 56cm= 2 \times \frac{22}{7} \times r \\ \\ \\ \large \sf \implies \: 56cm= \frac{44}{7} \times r \\ \\ \\ \large \sf \implies \: 56cm \times \frac{7}{44} = r \\ \\ \\ \large \sf \implies \: \cancel{ 56} \: \: 14cm \times \frac{7}{ \cancel{44} \: \: 11} = r \\ \\ \\ \large \sf \implies \:14cm \times \frac{7}{11} = r \\ \\ \\ \large \sf \implies \: \frac{98}{11} = r \\ \\ \\ \large \implies \sf \: 8.9090909.. = r\\ \\ \\ \large \implies \sf \: 8. \bar{90}= r \\ \\ \\ \large \star\rm \: \underline{ \underline{ round \: \: off : }}$

$\large \sf \boxed{ \therefore \: \sf \: radius = 8.91cm }$

Now ,

Finding Diameter :

$\\ \large \sf {diameter = 2 \times radius} \\ \\ \large : \implies \sf \: diameter = 2 \times 8.91 \\ \\ \large \boxed{ \underline{ \sf \: diameter = 17.82cm}}$

Question :

Find :

• Area

• Perimeter

• Radius

• Diameter

$\:$

$\large \star \: \red{ \boxed{ \green{ \sf answer : }}}$

$\large \leadsto\gray{ \rm \: area = 196 {cm}^{2} } \\ \\ \large \leadsto\gray{ \rm \: perimeter =56cm } \\ \\ \large \leadsto\gray{ \rm \: radius = 8.91cm} \\ \\ \large \leadsto\gray{ \rm \: diameter = 17.82cm }$