Question

ID.pdf
27. There are two wires each of length 88 cm. One is bent to form a square and the
other is bent to form a circle. Find which one of them has more area ?( Take II =
22
7​

Answer 1

$\bf \: \underline{{Given}} :$ ↴

$\sf \: There \: are \: two \: wires \: each \: of \: them \: are \: 88 \: cm\: in \: length.$

$\sf \: One \: is \: bent \: to \: form \: a \: square \: and \: the \: other \: is \: bent \: to \: form \: a \: circle.$

$\bf \: \underline{ To \: find }:$ ↴

$\sf \: We \: have \: to \: find \: that, find \: which \: shape \: has \: more \: area.$

$\bf \: \underline{\underline{Solution}} :$ ↴

$\sf \: First \: of \: all \: we \: will \: find \: the \: area \: of \: the \: Square.$

$\sf \: For \: that \: we \: have \: to \: find \: its \: side.$

$\sf \: Perimeter \: of \: square = 4 \times side$

$\sf \implies \: \: 88 = 4 \times side$

$\sf \implies \: Side = \dfrac{88}{4}$

$\sf \implies \: Side = 44 \: cm \:$

$\sf \: Area \: of \: square = S \: \times \: S$

$\sf \implies \: \: 22 \times 22$

$\sf \implies \: \: 484 \:$

$\red{ \sf \: So, \: Area \: of \: square \: is \: 484 \: cm ^{2}}$

$\sf \: Now, \: we \: will \: find \: the \: area \: of \: the \: circle.$

$\sf \: For \: that \: we \: have \: to \: find \: its \: radius.$

$\sf \: Perimeter \: of \: circle = length \: of \: the \: wire.$

$\sf \: Perimeter \: of \: circle = 88 \: cm$

$\sf \: Perimeter \: of \: circle = 2 \pi r$

$\sf \implies \:88 \: cm= 2 \times \dfrac{22}{7} \: \times r$

$\sf \implies \: \dfrac{88 \: cm}{2} = \dfrac{22}{7} \: \times r$

$\sf \implies \: 44 \: cm = \dfrac{22}{7} \: \times r$

$\sf \implies \: 44 \: cm \times \dfrac{22}{7} = r$

$\sf \implies \: 14 \: cm = r$

$\sf \: Radius \: of \: the \: circle = 14 \: cm$

$\sf \: Area \: of \: circle = \pi r ^{2}$

$\sf \implies \: \dfrac{22}{7} \: \times 14^{2}$

$\sf \implies \: \dfrac{22}{7} \times 196$

$\sf \implies \: 616$

$\red{ \sf \: So, \: Area \: of \: circle \: is \: 614 \: cm ^{2}}$

$\boxed{ \sf \: 484 \: cm ^{2} < 616 \: cm ^{2}}$

$\underline{ \boxed{ \pink{\sf \: So, \: the \: circle \: has \: more \: area \: than \: the \: square. }}}$