Question

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 10 minutes

Answer 1

$\sf{Angle \: made \: by \: minute \: hand \: in \:} \\ \\ { \sf{1m \: = \frac{360°}{60°} = 6°} }$

$\\ \sf{Angle \: made \: by \: minute \: hand \: in} \\ \\ { \sf10 \: m = 10 \times 6° = 60° \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\sf{The \: area \: swept \: by \: minute \: hand \: is \: in \: the \:shape \: of \: a \: sector \: with \: radius}$

$\sf{r \: = 14 \: cm \: and \: x° = 60 °}$

$\boxed{ \boxed{ \rm{Area \: = \: \frac{x}{360} \times \pi {r}^{2} } }}$

$\\ = \rm{ \frac{60}{ 360} \times \frac{22}{7} \times 14 \times 14 }$

$\\ = \rm{ \frac{1}{6} \times 616 }$

$\\ = 102.66 \: \rm{ {cm}^{2} }$

$\\ \sf{ \therefore \: area \: swept \: by \: the \: minute \: hand \: in \: 10 \: minutes \: = \: 102.66 \: {cm}^{2} }$

Answer 2

Step-by-step explanation:

length of minute hand of clock, radius, r =14cm

angle sweapt by hand clock in 60 minutes =360 degree

angle swept by hand clock in 1 minute =360/60 =6degree

angle made in 10 minute = 6*10,theta =60degree

area swept by hand clock in 10 minutes =area of sector =theta /360*πr2

60/360 *22/7*14*14

=308/3 =102.67cm2 (approx)