Question

A copper wire is bent in the form of a square of side 44cm. If it is re-bent in the form
of a circle, then find the following: (Take = 22 ) 7
a) The perimeter of the square
b) The circumference of the circle
c) The radius of the circle
d) Area of the circle.

Answer 1

SOLUTION

a) The perimeter of the square

Perimeter of the square = 4a

Side of the square(a) = 44cm.

⇒ Perimeter = 4 × 44

⇒ Perimeter = 176 cm.

b) The circumference of the circle

Circumference of the Circle = Perimeter of the square

⇒ Circumference of the Circle = 176cm.

c) The radius of the circle

Circumference of a circle = 2πr

Here,

Circumference = 176cm.

$\implies \sf Circumference = 2*\pi *r$

$\implies$ 176 = 2πr

$\implies \sf \pi r =\dfrac{176}{2}$

$\implies \sf \pi r= 88$

$\implies \sf 22r = 88*7$

$\implies \sf 22r = 616$

$\implies \sf r = \dfrac{616}{22}$

∴ Radius (r) = 28cm.

d) Area of the circle.

Area of a circle = πr²

Here,

r = 28cm.

$\implies \sf Area \: of\: the \: circle = \dfrac{22}{7} * 28^2$

$\implies \sf Area \: of\: the \: circle = \dfrac{22}{7} * 784$

$\implies \sf Area \: of\: the \: circle = 22 * 112$

$\implies \sf Area \: of\: the \: circle = 2464 cm^2.$

Answer 2

Yᴏᴜʀ Qᴜᴇsᴛɪᴏɴ

• A copper wire is bent in the form of a square of side 44 cm. If it is re-bent in the form of a circle, then find the following : -
• a) The perimeter of the square.
• b) The circumference of the circle.
• c) The radius of the circle.
• d) Area of the circle.

Rᴇǫᴜɪʀᴇᴅ Aɴsᴡᴇʀ.

$\\ \large{ \frak ✧\:\:{ \underline { \: \:{ \color{purple}{ \frak { a) \: \: The \: perimeter \: of \: the \: square \: : - }}}}}}$

$\dag \: \: \sf \underline {As \: we \: know \: that \: : - \tt  Perimeter \: of \: square \: = \: 4 \times side.}$

$\tt \underline{ : \implies \: perimeter \: _ { \sf \color{violet}(square)} \: = \:4 \: \times \: side }$

$\tt \underline{ : \implies \: perimeter \: _ { \sf \color{violet}(square)} \: = \:4 \: \times \: 44 \: cm }$

$\underline{\boxed{\tt { : \implies \: p \: = \:{ \color{purple} \: 176 \: cm .}}}}$

$\large{ \frak ✧\:{ \underline { \: \:{ \color{purple}{ \frak { b) \: \: The \: circumference \: of \: the \: circle \: : - }}}}}}$

$\dag \: \: \sf \underline {As \: we \: know \: that \: : - \tt \:Circumference \: of \: circle \:  = \:  Perimeter \: of \: square}$

$\tt \underline {: \implies{Circumference \:_{ \sf \color{violet}( circle )}\:  = \:  Perimeter \: _{ \sf \color{violet}( square)}}}$

$\underline{\boxed{\tt {: \implies\:C \:  = \: { \color{purple}{176 \: cm} \: }}}}$

$\large{ \frak ✧\:\:{ \underline { \: \:{ \color{purple}{ \frak { c) \: \: The \: Radius \: of \: the \: circle \: : - }}}}}}$

$\dag \: \: \sf \underline {As \: we \: know \: that \: : - \: \: { \boxed{ \tt{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{c \: _{ \sf \color{violet}(circumference)}}{2 \times \pi}}}} }$

$\tt \underline{ : \implies{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{c \: _{ \sf \color{violet}(circumference)}}{2 \times \pi}} }$

$\tt \underline{ : \implies{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{176 \: cm \: _{ \sf \color{violet}(circumference)}}{2 \: \times \frac{22}{7} }} }$

$\tt \underline{ : \implies{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{176 \: cm \: _{ \sf \color{violet}(circumference)}}{ \dfrac{2 \: \times \: 22}{7} }} }$

$\tt \underline{ : \implies{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{176 \: cm \: _{ \sf \color{violet}(circumference)}}{ \dfrac{44}{7} }} }$

$\tt \underline{ : \implies{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{176 \: cm \: \times \: 7}{44 }} }$

$\tt \underline{ : \implies{\:r \:_{ \sf \color{violet}(radius)} \: = \: \frac{1232}{44 }} }$

$\underline{ \boxed{ \tt{ : \implies{ \purple{\:r \: \: = \: 28}}} }} \: \: \bigstar$

$\large{ \frak ✧\:\:{ \underline { \: \:{ \color{purple}{ \frak { d) \: \: The \: Area\: of \: the \: circle \: : - }}}}}}$

$\dag \: \: \sf \underline {As \: we \: know \: that \: : - \: \: { \boxed{ \tt{\:a \:_{ \sf \color{violet}(area \: of \: circle)} \: = \: \pi \: r {}^{2} }}} }$

${ \underline{ \tt{ : \implies\:a \:_{ \sf \color{violet}(area \: of \: circle)} \: = \: \pi \: r {}^{2} }}}$

${ \underline{ \tt{ : \implies\:a \:_{ \sf \color{violet}(area \: of \: circle)} \: = \: \frac{ 22 }{ 7 } \times 28 ^ { 2 } }}}$

${ \underline{ \tt{ : \implies\:a \:_{ \sf \color{violet}(area \: of \: circle)} \: = \: \frac{22}{7}\times 784 }}}$

${ \underline{ \tt{ : \implies\:a \:_{ \sf \color{violet}(area \: of \: circle)} \: = \: \frac{22\times 784}{7} }}}$

${ \underline{ \tt{ : \implies\:a \:_{ \sf \color{violet}(area \: of \: circle)} \: = \: \frac{17248}{7} }}}$

${ \underline{ \boxed{ \tt{ : \implies\:{ \purple{a \: = \: 2464 }}}}}} \: \: \bigstar$

✯ Hope it helps u ✯