# The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes

**Solution:**

We use the formula for the area of the circle to find the area swept by the minute hand.

We know that the minute hand completes one rotation in 1 hour or 60 minutes.

Therefore, area swept by the minute hand in 60 minutes = Area of the circle with radius equal to the length of the minute hand = πr^{2}

Using unitary method, we get

Area swept by minute hand in 1 minute = πr^{2}/60

Thus, area swept by minute hand in 5 minutes = (πr^{2}/60) × 5 = πr^{2}/12

Length of the minute hand (r) = 14 cm

It is known that the minute hand completes one rotation in 1 hour or 60 minutes

Therefore, the area swept by the minute hand in 60 minutes = πr^{2}

Therefore, the area swept by the minute hand in 5 minutes = 5/60 × πr^{2} ⇒ 1/12 πr^{2}

= 1/12 × 22/7 × 14 × 14 cm^{2}

= 154/3 cm^{2}

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 12

**Video Solution:**

## The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 3

**Summary:**

The area swept in 5 minutes by the minute hand of length 14 cm of a clock is 154/3 cm^{2}.

**☛ Related Questions:**

- A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use π = 3.14)
- In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:(i) the length of the arc(ii) area of the sector formed by the arc(iii) area of the segment formed by the corresponding chord
- A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
- A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73)

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