Question

The length of the minute hand of a clock is 14cm . find the area swept by the minute hand in 15 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

Hence the area swept by the minute hand clock in 1 min =61660 square centimetres. Hence the area swept by the minute hand of the clock in 15 minutes =61660×15=154 square centimetres, which is the same as obtained above.