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0 votes
39.8k views
in Mensuration by (44.3k points)

The minute hand of a clock is 15 cm long. Calculate the area swept by it in 20 minutes.

2 Answers

+1 vote
by (58.8k points)
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Best answer

The minute hand of a clock is 15 cm long

Angle described by the minute hand in 60 minutes = 360°

Angle described by minute hand in 20 minutes = 360/60 x 20 = 120°

So, area swept by it in 20 minutes = Area of the sector having central angle 120° and radius 15 cm

= θ/360 (πr2)

= 120/360 x 22/7 x 15 x 15

= 235.5

Therefore, the area swept by minute hand in 20 minutes is 235.5 cm2.

+1 vote
by (1.7k points)
Answer:

235.5‬ cm²

Step-by-step explanation:

The minute hand is 15 cm long. So the radius of the circle the minute hand makes will be 15 cm.

Area swept in 60 minutes = Area of a circle

Area of a circle  =  π r² = 3.14 * 15 * 15 = 706.5 cm²

The minute hand make a complete circle in 1 hour or 60 minutes.

in 20 minutes, the minute hand makes 20/60  = 1/3 circle.

∴Area swept by the minute hand in 20 minutes = 1/3 * area swept in 60 minutes.​

Area swept by the minute hand in 20 minutes = 1/3 * 706.5

Area swept by the minute hand in 20 minutes = 235.5‬ cm²

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