Question

A wire in the form of a square with side 22 cm. It is reshaped and bent into the form of a circle. Calculate the area of this circle.​

Answer 1

given that side of the square is 22 cm

perimeter of the square =4a

=4×22cm

=88 cm

as the same wire is used to form a circle then both will have same perimeter.

perimeter of circle = perimeter of square

⇒2πr=88

⇒2× 7/22

r=88

⇒r= 22×2/88×7

⇒r=14 cm

hence radius of the circle is 14cm.

then,

area of the circle =πr^2

=7/22 ×14×14cm ^2

=616 cm^2

Answer 2

$\huge\mathcal{\fbox{\fbox \mathtt{\orange{answer}}}}$

Given that side of the square is 22 cm

Perimeter of the square =4a

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ =4×22cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ =88 cm

★ As the same wire is used to form a circle then both will have same perimeter.

$\sf\green \bigstar \blue{perimeter \: of \: circle = perimeter \: of \: square}$

So,

$\implies \mathtt \red{2\pi \:r = 88}$

$\implies \mathtt \red{2 \times \frac{22}{7} r = 88}$

$\implies \mathtt \red{r = \frac{88 \times 7}{22 \times 2}}$

$\implies \mathtt \red{r = 14 \: cm}$

Hence radius of the circle is 14cm.

then,

$\sf\green \bigstar \blue{area \: of \: the \: circle = \pi \: r {}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf\pink{ = \frac{22}{7} \times 14 \times 14 \: cm {}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small\blue\star\underbrace\mathtt{\underline{\underline\red{ = 616 \: cm {}^{2} }}}$