The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 a m and 6 : 40 a m
Solution:
Given, the length of the minute hand of a clock is 5 cm.
We have to find the area swept by the minute hand during the time period 6:05 am and 6:40 am.
In one hour (60 mins), the minute hand revolves 360°
In one minute, the minute hand revolves 360°/60° = 6°
The time gap between 6:05 am and 6:40 am = 35 mins
In 35 minutes, minute hand revolves = 6° × 35
= 210°
From the figure,
The area swept by the minute hand in the given time period represents a sector of a circle.
Here, corresponding angle θ = 210°
Radius = 5 cm
Area of sector = πr²θ/360°
= (22/7)(5)²(210°/360°)
= (22/7)(25)(7/12)
= (22)(25)/12
= 11(25)/6
= 45.83 cm²
Therefore, the area swept by the minute hand is 45.83 cm²
✦ Try This: The length of the minute hand of a clock is 4 cm. Find the area swept by the minute hand during the time period 4 : 05 a m and 5 : 00 a m.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 14
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 a m and 6 : 40 a m
Summary:
The length of the minute hand of a clock is 5 cm. The area swept by the minute hand during the time period 6 : 05 a m and 6 : 40 a m is 45.83 cm²
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