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.
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