Question

if hour of a circular clock is 7cm long ,then find the area swept by it in 36 min​

Answer 1

$\huge{\bold{\underline{\underline{Question:-}}}}$

If hour hand of a circular clock is 7cm long, then find the area swept by it in 36 min.

$\huge{\bold{\underline{\underline{Solution:-}}}}$

Angle moved by the hour hand in 1 hour

$= \frac{5}{60} \times 360$

$= \frac{360}{12}$

$= 30\degree$

Angle made by hour hand in 60 min = 30°

Angle made by hour hand in 1 min = 30°/60° = 1/2

Angle made by hour hand in 36 min = 1/2 * 36

= 18°

Area of sector

$\frac{ \theta }{360} \times {\pi \: r}^{2}$

$= \frac{18}{360} \times \frac{22}{7} \times {7}^{2}$

$= \frac{1}{20} \times \frac{22}{7} \times 49$

$= \frac{1}{ \cancel {20} } \times \frac{ \cancel {22}} {7} \times 49$

$= \frac{1}{10} \times \frac{11}{ \cancel {7}} \times \cancel{49}$

$= \frac{1}{10} \times 11 \times 7$

$= \frac{77}{10}$

$= {7.7cm}^{2}$

Answer 2

\huge{\bold{\underline{\underline{Question:-}}}}

Question:−

If hour hand of a circular clock is 7cm long, then find the area swept by it in 36 min.

\huge{\bold{\underline{\underline{Solution:-}}}}

Solution:−

Angle moved by the hour hand in 1 hour

= \frac{5}{60} \times 360=

60

5

×360

= \frac{360}{12}=

12

360

= 30\degree=30°

Angle made by hour hand in 60 min = 30°

Angle made by hour hand in 1 min = 30°/60° = 1/2

Angle made by hour hand in 36 min = 1/2 * 36

= 18°

Area of sector

\frac{ \theta }{360} \times {\pi \: r}^{2}

360

θ

×πr

2

= \frac{18}{360} \times \frac{22}{7} \times {7}^{2}=

360

18

×

7

22

×7

2

= \frac{1}{20} \times \frac{22}{7} \times 49=

20

1

×

7

22

×49

= \frac{1}{ \cancel {20} } \times \frac{ \cancel {22}} {7} \times 49=

20

1

×

7

22

×49

= \frac{1}{10} \times \frac{11}{ \cancel {7}} \times \cancel{49}=

10

1

×

7

11

×

49

= \frac{1}{10} \times 11 \times 7=

10

1

×11×7

= \frac{77}{10}=

10

77

= {7.7cm}^{2}=7.7cm

2