Question

the length of the minute hand of a clock is 14 cm find the area swept by the minute hand in 5 minutes.

​

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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Length of minute hand = radius of the clock (circle)

∴ Radius (r) of the circle = 14 cm (given)

Angle swept by minute hand in 60 minutes = 360°

So, the angle swept by the minute hand in 5 minutes = 360° × 5/60 = 30°

We know,

Area of a sector = (θ/360°) × πr2

Now, area of the sector making an angle of 30° = (30°/360°) × πr2 cm2

= (1/12) × π142

= (49/3)×(22/7) cm2

= 154/3 cm2