Question

the lenth if mintute hand of clock is 14cm . the area swept by the minute hand in one minute

​

Answer 1

Answer:

Minute hand completes full circle degree in 60 minutes.

Angle swept by minute in 60 minutes =360°

Angle swept by the minute hand in 15 minutes =

60

360°

×15=90°

Therefore,

θ=90°

Length of minute hand =r=14cm

Area swept by minute hand in 15 minutes = Area of sector

As we know that area of sector is given as-

A=

360°

θ

×πr

2

Therefor,

Area swept by the minute hand in 15 minutes =

360°

90°

×(

7

22

×(14)

2

)=

4

1

×616=154cm

2

Hence the area swept by the minute hand in 15 minutes is 154cm

2

.

Hence the correct answer is 154cm

2

.

Answer 2

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

[Use π = $\frac{22}{7}$ ]

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=> 10.26 cm².

$\large \displaystyle{\boxed {\sf{ \displaystyle {Step-by-step \: explanation \: :}}}}$

Length of minute hand = 14 cm

Now, angle made by minute hand in 1 min =

$\frac{360^0}{60^0}$ = ${60^0}$

∴ area swept by minute hand = $\frac{6^0}{360^0}$ × πr²

$\frac{6^0}{360^0}$ × $\frac{26}{7}$ × 14 × 14

= $\frac{154}{15}$ = 10.26 cm²