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.

(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 ${40}^{\circ }$?

$\begin{array}{cccccc}Numberofspokes& 4& 6& 8& 10& 12\\ Anglebetweenapairofconsecutivespokes\left(Indegrees\right)& 90& 60& & & \end{array}$
[3 MARKS]

Answer 1

Solution: 1 Mark each

Here the constant $k=4\times {90}^{\circ }={360}^{\circ }$

Hence, Angle for 8 spokes
$=\frac{\left({360}^{\circ }\right)}{8}={45}^{\circ }$

Angle for the 10 spokes
$=\frac{\left({360}^{\circ }\right)}{10}={36}^{\circ }$

Angle for the 12 spokes
$=\frac{\left({360}^{\circ }\right)}{12}={30}^{\circ }$

i) With increasing number of spokes the angle is decreasing so they are in inverse proportion.

ii) $\frac{360}{15}={24}^{\circ }$ is the angle between the spokes.

iii) $\frac{\left({360}^{\circ }\right)}{Spokes}={40}^{\circ }$

$\Rightarrow spokes=\frac{{360}^{\circ }}{{40}^{\circ }}=9$