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:

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Step-by-step explanation:

In 60 minutes, minute hand completes 360

0

i.e., one rotation.

⇒ in 1 minute, minute hands completes

60

360

∘

=6

∘

Hence, in 5 minutes the angle covered is is 6×5=30

o

.

The angle of sector formed is 30

o

.

The area swept by the minute hand in 5 minutes=

360

30

×π×14×14

Using π=

7

22

, we get

The area swept by the minute hand in 5 minutes =

3

154

sq. cm

Answer 2

Given:

• The length of the minute hand of a clock is 14 cm

To Find:

• Find the area swept by the minute hand in 5 minutes.

Solution:

• Radius of clock = 14cm
• Angle swept in 1 hour = 360
• Angle swept in 1 min = 360/6 = 6°
• Angle swept in 5 min= 6 × 5 = 30°

Area swept by a minute = θ/360° × πr²

→ 30°/360 × 22/7 × 14 × 14

→ 22 × 2 × 14/12

→ 154/3 cm²

• Hence, area swept by the minute hand in 5 minutes is 154/3 cm²

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