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Question 03.
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:
No.of spokes4681012Angle between a pair of consecutive spokes9060


(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40 ?
 


Solution

Here the number of spokes are increasing and the angle between a pair of consecutive spokes is decreasing. So, it is a inverse proportion and angle at the centre of a circle is 360 .
When the number of spokes is 8,
then angle between a pair of consecutive spokes = 3608=45
When the number of spokes is 10,
then angle between a pair of consecutive spokes = 36010=36
When the number of spokes is 12,
then angle between a pair of consecutive spokes = 36012=30
No.of spokes4681012Angle between a pair of consecutive spokes9060453630

(i) Yes, the number of spokes and the angles formed between a pair of consecutive spokes is in inverse proportion.
(ii) When the number of spokes is 15, then angle between a pair of consecutive spokes =36015=24
(iii) The number of spokes would be needed = 36040=9

 

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