NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.2 Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Understanding of Directly Proportional and Inversely Proport …

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:

Table Shows No. Of Spokes and Angle between a Pair of Consecutive Spokes
No. of spokes
Angle between a pair of consecutive spokes________________________
Making a Wheel Using 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

Showing Table of No. Of Spokes and 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