Question

The length Of minute hand of a clock is 21 cm. find the area swept by the clock in 2 minutes

Answer 1

Answer:

A = 45.7cm²

Step-by-step explanation:

r = 21cm. theta (ô) = 12°

A = ô/360° πr²

= 12/360 [3.14(21)(21)]

= 0.033 [3.14(21)(21)]

= 45.7cm²

Answer 2

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

$\tt The\: length\: of\: minute\: hand\: of\: a\: clock\: is\: 21\: cm.\\\tt find\: the \:area\: swept \:by\: the\: clock\: in\: 2 \:minutes.$

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

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

$\bf Length\: of\: the\: minute\: hand = 21\: cm$

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

$\bf Area \:swept\: by\: the \:minute\:hand \: in\: 2\: minutes$

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

$\sf\leadsto In\: one \:hour \:minute\: hand\: completes\: full\: rotation$

$\sf \leadsto Swept\: by\: the\: minute\: hand\: in\: 60\:minutes ={360}^{\circ}$

$\sf\leadsto Swept \:by\: the\: minute\: hand\: in\: 1\:minute$

$\bf \implies \dfrac{360}{60}$

$\bf \implies \dfrac{\cancel{360}}{\cancel{60}}$

$\implies {\blue {\boxed {\boxed {\purple {\sf {{6}^{\circ}}}}}}}$

$\sf\leadsto Swept\: by\: the\: minute\: hand\: in \:2\:minutes$

$\bf \implies 2 \times {6}^{\circ}$

$\implies {\blue {\boxed {\boxed {\purple {\sf {\theta={12}^{\circ}}}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {A_{(Sector)}=\dfrac{\theta}{{360}^{\circ}}\pi{r}^{2}}}}}}}}$

• $\sf A=area\: of\: the\: sector$
• $\sf r=radius\: of\: the\: minute\: hand$

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

$\bf \implies A=\dfrac{12}{360}\times \dfrac{22}{7}\times {\big(21\big)}^{2}$

$\bf \implies A=\dfrac{\cancel{12}} {\cancel{360}}\times \dfrac{22}{\cancel{7}}\times 21\times \cancel{21}$

$\bf \implies A=\dfrac{1}{30}\times 22\times 21\times 3$

$\bf \implies A=\dfrac{1}{\cancel{30}}\times 22\times 21\times \cancel{3}$

$\bf \implies A=\dfrac{1}{10}\times 22\times 21$

$\bf \implies A=0.1\times 462$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {A=46.2\:{cm}^{2}}}}}}}$