  Question

# 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 spokes90∘60∘……… (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 = 360∘8=45∘ When the number of spokes is 10, then angle between a pair of consecutive spokes = 360∘10=36∘ When the number of spokes is 12, then angle between a pair of consecutive spokes = 360∘12=30∘ No.of spokes4681012Angle between a pair of consecutive spokes90∘60∘45∘36∘30∘ (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 =360∘15=24∘ (iii) The number of spokes would be needed = 360∘40∘=9  Suggest corrections   