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 = πr²

Using unitary method, we get

Area swept by minute hand in 1 minute = πr²/60

Thus, area swept by minute hand in 5 minutes = (πr²/60) × 5 = πr²/12

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 = πr²

Therefore, the area swept by the minute hand in 5 minutes = 5/60 × πr² ⇒ 1/12 πr²

= 1/12 × 22/7 × 14 × 14 cm²

= 154/3 cm²

☛ 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 cm².

☛ 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)