Question

à ῳıཞe ıŋ ɬɧe ʂɧą℘e ơʄ ą ཞeƈɬąŋɠƖe ῳıɬɧ ɬɧe ʂıɖeʂ 14ƈɱ ąŋɖ 8ƈɱ ıʂ ʂɬཞąıɠɧɬeŋeɖ ąŋɖ ɬɧeŋ ცeŋɬ ıŋ ɬɧe ʂɧą℘e ơʄ ą ƈıཞƈƖe ʄıŋɖ ɬɧe ཞąɖıųʂ ąŋɖ ɬɧe ąཞeą ơʄ ą ƈıཞƈƖe ??? Please tell the correct ones

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt A \:wire\: in\: the\: shape\: of\: a\: rectangle\: with\: the\: sides\\\tt 14\:cm\: and\: 8\:cm \:is\: straightened\: and\: then\: bent\: in\\\tt the\: shape\: of \:a \:circle. \:Find\: the\: radius\: and\\\tt the\: area\: of\: the\: circle.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\bf Length\: of \:the\: rectangle =14\:cm$
• $\bf Breadth\: of \:the\: rectangle =8\:cm$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\bf Radius\: of \:the\: circle$
• $\bf Area\: of \:the\: circle$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Radius \:of \:the \:circle(r)}}}}}$

${\leadsto {\orange {\sf {Perimeter\: of \:the\: rectangle(P)}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {P_{(Rectangle)}=2\big(l+b\big)}}}}}}}$

• $\sf P=perimeter\:of the \:rectangle$
• $\sf l=length\:of the \:rectangle$
• $\sf b=breadth\:of the \:rectangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies P=2\big(14+8\big)$

$\bf \implies P=2\big(22\big)$

$\implies {\blue {\boxed {\boxed {\purple {\sf {P=44\:cm}}}}}}$

${\blue {\boxed {\green {\sf {Perimeter\: of\: the\: rectangle = Circumference \:of\: the\: circle}}}}}$

${\leadsto {\orange {\sf {Radius\: of \:the\: circle(r)}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {C_{(Circle)}=2\pi r}}}}}}}$

• $\sf C=circumference\:of the \:circle$
• $\sf r=radius\:of the \:circle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies 44=2\times \dfrac{22}{7}\times r$

$\bf \implies 44=\dfrac{44}{7}\times r$

$\bf \implies 44\times 7=44r$

$\bf \implies 308=44r$

$\bf \implies r=\dfrac{308}{44}$

$\bf \implies r=\dfrac{\cancel{308}}{\cancel{44}}$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {r=7\:cm}}}}}}$

${\underbrace {\red {\underline {\red {\overline {\red {\pmb {\sf {{\therefore} The\:radius\: of \:the\: circle\: is \:7 \:cm}}}}}}}}}$

———————————————————————————————

${\pink {\underline {\bf {\pmb {Area \:of \:the \:circle(A)}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {A_{(Circle)}=\pi{r}^{2}}}}}}}}$

• $\sf A=area\:of the \:circle$
• $\sf r=radius\:of the \:circle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies A=\dfrac{22}{7}\times {\big(7\big)}^{2}$

$\bf \implies A=\dfrac{22}{7}\times 7\times 7$

$\bf \implies A=\dfrac{22}{\cancel{7}}\times 7\times \cancel{7}$

$\bf \implies A=22 \times 7$

$\implies{\blue {\boxed {\boxed {\purple {\mathfrak {A=154\:{cm}^{2}}}}}}}$

${\underbrace {\red {\underline {\red {\overline {\red {\pmb {\sf {{\therefore} The\:area\: of \:the\: circle\: is \:154\:{cm}^{2}}}}}}}}}}$

____________________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

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

$\sf Circumference\:of \:the \:circle =2\pi r$

$\sf Diameter \:of \:the \:circle =2r$