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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

The angle between a pair of consecutive spokes

90°

60°

–

–

–
(i) Are the number of spokes and the angle 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°?



Answer -

From the above table, we observe that
4 × 90° = 6 × 60°
360° = 360°
Thus the two quantities are inversely proportional.
Let the blank spaces be denoted by a, b, and c.
4 × 90° = 8 × a

Hence, the requiredtable is

Number of spokes

4

6

8

10

12

The angle between a pair of consecutive spokes

90°

60°

45°

36°

30°

(i) Yes, they are ininverse proportion
(ii) If the number of spokes is 15, then
4 × 90° = 15 × x
x = (4×90)/15 = 24°
(iii) If the angle between two consecutive spokes is 40°, then
4 × 90° = y × 40°
y = (4×90)/40 = 9 spokes.
Thus the required number of spokes = 9.

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