Question

If the circumference of a circle is 198 cm find its radius and diameter​

Answer 1

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

$\tt If \:the\: circumference\: of \:a \:circle\: is\: 198\: cm\: find\: its\\\tt radius \:and \:diameter.$

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

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

• $\sf \bf Circumference \:of \:the \:circle = 198\:cm$

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

• $\sf \bf (i) Radius \:of \:circle$
• $\sf \bf (ii) Diameter \:of \:circle$

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

${\color{springgreen} \underline {\sf (i) Radius \:of \:circle}}$

${\boxed {\boxed {\boxed {\color {blue} {\sf \bf C=2 \pi r}}}}}$

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

${\underbrace {\overbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

$\sf \bf \implies 198 = 2 \times \dfrac{22}{7} \times r$

$\sf \bf \implies 198\times 7=2 \times 22 \times r$

$\sf \bf \implies 1386 = 44r$

$\sf \bf \implies r = \dfrac{1386}{44}$

$\implies {\boxed {\boxed {\color {aqua} {\sf \bf r=31.5\:cm}}}}$

${\underbrace {\color {red} {\underline {\color {red} {\overline {\color {red} {\sf \therefore The\:radius \:of\:the \:circle \:is\:31.5 \:cm}}}}}}}$

—————————————————————————————

${\color{springgreen} \underline {\sf (ii) Diameter \:of \:circle}}$

${\boxed {\boxed {\boxed {\color {blue} {\sf \bf D=2 r}}}}}$

• $\sf D=diameter \:of \:the \:circle$
• $\sf r=radius \:of \:the \:circle$

${\underbrace {\overbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

$\sf \bf \implies D=2 \times 31.5$

$\implies {\boxed {\boxed {\color {aqua} {\sf \bf D=63\:cm}}}}$

${\underbrace {\color {red} {\underline {\color {red} {\overline {\color {red} {\sf \therefore The\:diameter\:of\:the \:circle \:is\:63 \:cm}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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

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

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

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

$\bf Radius \:of \:the \:circle =\dfrac{D}{2}$

Answer 2

$\blue{\bold{\underline{\underline{}}}}$

Hope It helps!