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Question
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table:
| Number of spokes | 4 | 6 | 8 | 10 | 12 |
| Angle between a pair of consecutive spokes |
90° | 60° | ... | ... | ... |
- Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
- Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
- How many spokes would be needed if the angle between a pair of consecutive spokes is 40°?
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Solution
- Number of sticks = 8
The angle between each pair of consecutive spokes = `360/8`
= 45° - Number of sticks = 10
The angle between each pair of consecutive spokes = `360/10`
= 36° - Number of sticks = 12 The angle between each pair of consecutive spokes is `360/12`
= 30°
| Number of spokes | 4 | 6 | 8 | 10 | 12 |
| Angle between a pair of consecutive spokes |
90° | 60° | 45° | 36° | 30° |
According to the question:
- Yes, the number of spokes and the angle between any pair of consecutive spokes are inversely proportional.
- Number of sticks = 15
Angle between each pair of consecutive spokes = `360/15`
= 24° - Given angle between each pair of consecutive spokes = 40°
number of sticks required will be = `360/40`
= 9
Hence, number of sticks required = 9
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