The length of a minute hand of a wall clock is 7 cm. What is the area ...
Explanation:-
The area covered by the minute hand in 60 minutes is equal to area of the circle of radius 7 cm
The area covered by minute hand in 30 minutes will be half of the area of the circle.
We know, area of the circle = π r^2
Half of the area of the circle = ½ π r^2
Here, π = 22/7 and r = 7
=> ½ *22/7 * (7) *(7)
=> 11 * 7
=> 77 cm square
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The length of a minute hand of a wall clock is 7 cm. What is the area ...
The length of a minute hand of a wall clock is 7 cm. What is the area ...
To find the area swept by the minute hand of a wall clock in 30 minutes, we need to calculate the angle swept by the minute hand and then use it to find the area.
1. Finding the angle swept by the minute hand:
- In 60 minutes, the minute hand completes a full revolution (360 degrees).
- So, in 1 minute, the minute hand sweeps an angle of 360 degrees / 60 = 6 degrees.
- Therefore, in 30 minutes, the minute hand will sweep an angle of 6 degrees * 30 = 180 degrees.
2. Finding the area swept by the minute hand:
- The area swept by an object moving in a circular path is given by the formula: Area = (θ/360) * π * r^2, where θ is the angle swept and r is the length of the object.
- Substituting the values, we get: Area = (180/360) * π * 7^2 = (1/2) * π * 7^2 = (1/2) * π * 49 = 24.5π.
- Since we need to provide the answer as a decimal, we can use an approximation for π as 3.14.
- Therefore, the area swept by the minute hand is approximately 24.5 * 3.14 = 76.93 cm^2.
3. Choosing the correct option:
- Among the given options, option B is 3.208.
- The calculated area of 76.93 cm^2 does not match any of the given options exactly.
- However, we can see that option B, 3.208, is the closest approximation to the calculated area.
- Therefore, option B is the correct answer.
In conclusion, the area swept by the minute hand of a wall clock in 30 minutes is approximately 76.93 cm^2, and the correct answer among the given options is B.
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