NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.2 Part 2
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Understanding of directly proportional and inversely proportional
1. 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 spokes | |||||
Angle between a pair of consecutive spokes | ____ | ___ | ___ |
(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 ?
Answer:
Here the numbers of spokes are increasing and the angle between a pair of consecutive spokes is decreasing.
So, it is an inverse proportion and angle at the centre of a circle is .
When the number of spokes is, then angle between a pair of consecutive spokes
When the number of spokes is, then angle between a pair of consecutive spokes
When the number of spokes is, then angle between a pair of consecutive spokes
No. of spokes | |||||
Angle between a pair of consecutive spokes |
(i) Yes, the number of spokes and the angles formed between a pair of consecutive spokes in inverse proportion.
(ii) When the number of spokes is, then angle between a pair of consecutive spokes
(iii) The number of spokes would be needed