(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 \(40^o\)?

Answer :

From the given table we have, \(4\times90^o=6\times60^o\)

\(\Rightarrow 360^o=360^o\)

Thus, we can say that quantities are inversely peoportional

Let the blacks be as a,b and c

So we have, \(4\times90^o=8\times a \)

\(\Rightarrow a=\frac{4\times 90^o}{8}=45^o\)

Similarly, \(4\times90^o=10\times b \)

\(\Rightarrow b=\frac{4\times 90^o}{10}=36^o\)

And, \(4\times90^o=12\times c \)

\(\Rightarrow c=\frac{4\times 90^o}{12}=30^o\)

Hence, we have the table as:

(i) Yes, they are in inverse proportion

(ii) If the number of spokes is 15, then

\(4 \times 90^o = 15 \times x\)

\(x = \frac { 4\times 90 }{ 15 } = 24^o\)

(iii) If the angle between two consecutive spokes is \(40^o\), then

\(4 \times 90^0 = y \times 40^o\)

\(y = \frac { 4\times 90 }{ 40 } = 9 spokes.\)

Thus the required number of spokes = 9.<\br>

- 1.Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled at a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person.
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- 8.A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
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- NCERT solutions for class 8 maths chapter 1 Rational Numbers
- NCERT solutions for class 8 maths chapter 2 Linear Equations in One Variable
- NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals
- NCERT solutions for class 8 maths chapter 4 Practical Geometry
- NCERT solutions for class 8 maths chapter 5 Data Handling
- NCERT solutions for class 8 maths chapter 6 Squares and Square Roots
- NCERT solutions for class 8 maths chapter 7 Cube and Cube Roots
- NCERT solutions for class 8 maths chapter 8 Comparing Quantities
- NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities
- NCERT solutions for class 8 maths chapter 10 Visualising Solid Shapes
- NCERT solutions for class 8 maths chapter 11 Mensuration
- NCERT solutions for class 8 maths chapter 12 Exponents and Powers
- NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions
- NCERT solutions for class 8 maths chapter 14 Factorization
- NCERT solutions for class 8 maths chapter 15 Introduction to Graphs
- NCERT solutions for class 8 maths chapter 16 Playing with Numbers

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- NCERT solutions for class 8 science chapter 2 Microorganisms: Friend and Foe
- NCERT solutions for class 8 science chapter 3 Synthetic Fibers and Plastics
- NCERT solutions for class 8 science chapter 4 Materials: Metals and Nonmetals
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- NCERT solutions for class 8 science chapter 6 Combustion and Flame
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- NCERT solutions for class 8 science chapter 12 Friction
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- NCERT solutions for class 8 science chapter 15 Some Natural Phenomena
- NCERT solutions for class 8 science chapter 16 Light
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