Question

the lenght of minute hand of a clock is 14cm. the area swept by the minute hand in 5 minutes is :a)153.9cm^2 (b)102.6cm^2 (c) 51.3cm^2 and (d)205.2cm^2​

Answer 1

We have to find the area swept by the minute hand of a clock which is 14 cm long in 5 minutes.

We know, The minute hand will turn 360° in one hour, and one hour is equal to 60 minutes.

∴ In 60 minutes, the minute hand turns 360°. So in one minute It would turn,

⇒ In 1 minute, it would turn 360/60 × 5

⇒ Angle, θ = 6 × 5

⇒ Angle, θ = 30°

So, In 5 minutes, the minute hand would turn 30°.

Imagine the clock as a circle of radius the length of the minute hand, so In that hypothetical circle, we have

• Radius of circle, r = 14 cm
• Angle, θ = 30°

Now, This is a sector and we have to find the area of this sector. So

⇒ Area of sector = πr²θ/360°

⇒ Area = 22/7 × 14 × 14 × 30/360

⇒ Area = 44 × 14 × 1/12

⇒ Area = 11 × 14 × 1/3

⇒ Area = 154 / 3

⇒ Area = 51.3 cm²

Hence, In 5 minutes, the area swept by the minute hand of length 14 cm is 51.3 cm².

∴ Option (C) is correct.

Answer 2

Answer

$\sf{We \: have \: to \: find \: the \: area \: swept \: by \: the \: minute \: hand \: of \: a \: clock \: which \: is \: 14 \: cm \: long \: in \: 5 \: minutes.}</p><p>$

We know, The minute hand will turn 360° in one hour, and one hour is equal to 60 minutes.

∴ In 60 minutes, the minute hand turns 360°. So in one minute It would turn,

$&#10238; \: \sf{In \: 1 \: minute \: , it \: would \: turn \: 360/60 × 5}$

$&#10228; \bf{Angle, θ = 6 × 5}$

$\green {\sf{Angle, θ = 30° }}$

$&#10143; \: \rm{So \: , In \: 5 \: minutes \: , the \: minute \: hand \: would \: turn \: 30°.}$

• Imagine the clock as a circle of radius the length of the minute hand, so In that hypothetical circle, we have

Radius of circle, r = 14 cm

Angle, θ = 30°

Now, This is a sector and we have to find the area of this sector. So

✒ Area of sector = πr²θ/360°

✒ Area = 22/7 × 14 × 14 × 30/360

✒ Area = 44 × 14 × 1/12

✒ Area = 11 × 14 × 1/3

✒ Area = 154 / 3

✒ Area = 51.3 cm²

• Hence, In 5 minutes, the area swept by the minute hand of length 14 cm is 51.3 cm².

• ∴ Option (C) is correct.

$\huge{&#10516;}\pink{\rm{Hence \: We \: Are \: Done !!}}$