Question

the minute of the hand clock is 5cm long.Find the area describe by the minute on the face of the clock betweem 7:00Am to 7:22Am.​

Answer 1

✪ Question :- the minute of the hand clock is 5cm long.Find the area describe by the minute on the face of the clock betweem 7:00Am to 7:22Am. ?

✰ Concept and formula used :-

➳ Minute hand of a clock Make an angle of 6° in one minute .

➳ Area of sector of circle is given by : - (Angle at centre/360°) * πr² .

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❁ Solution :-

it is given that, Minute hand travel from 7:00 AM to 7:22 AM .

So,

→ it travel = 7:22 - 7:00 = For 22 minutes .

So,

→ Angle he made = 22 * 6 = 132° .

Now, Area of sector he made ,

⟿ Area = (132/360) * π * (5)²

⟿ Area = 0.367 * 3.14 * 25

⟿ Area = 28.80cm² . (Aprrox)

Hence, the minutes hand describe the area of 28.80cm² in given time..

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❦❦ Extra Brainly knowledge ❦❦:-

☛ The dial of the clock is circular in shape and was divided into 60 equal minute spaces..

☛ 60-minute spaces trace an angle of 3600. Therefore, 1minute space traverses an angle of 60..

☛ In 1 hour, Minute hand traverses 60-minute space or 3600 , Hour hand traverses 5-minute space or 300..

☛ The hands of the clock are perpendicular in 15-minute spaces apart....

☛ The hands of the clock are in straight line and opposite to each other in 30-minute spaces apart.

☛ The hands of the clock are in straight line when they coincide or opposite to each other.

☛ The hands of the clock are perpendicular to each other for 22 times in 12 hours and for 44 times in a day.

☛ The hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.

☛ The minute hand gain 55 minutes over hour hand per hour.

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Answer 2

Question :

The minute of the hand clock is 5cm long.Find the area swept by the minutes hand on the face of the clock betweem 7:00Am to 7:22A

Solution :

• The length of the minute's hand is 5 cm

To finD

• Area swept by the minute's hand between 7:00 and 7:22

$\rule{300}{2}$

We would need to find the angle between 7:00 and 7:22

• The minute hand sweeps 360° in 60 minutes

• Implies,it would cover 6° in one minute

In 22 minutes,∅ = 22 × 6 = 132°

$\rule{300}{2}$

The minute's hand forms an arc between 7:00 and 7:22

$\boxed{\boxed{\sf{ Area \ of \ an \ arc = \dfrac{ \theta}{360} \times \pi {r}^{2} }}}$

Substituting the values,we write :

$\longrightarrow \: \sf \dfrac{132}{360} \times {5}^{2} \times 3.14 \\ \\ \longrightarrow \: \sf \: 28.78 \: {cm}^{2}$

The area swept by the minute's hand between 7:00 and 7:22 is 28.78 cm²