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∘ ?

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

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

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