Please note that the options for the graphs are missing in the question posted. However, I will try my best to answer the question as there is just one graph that is possible.
Please find the two attached diagrams to get a better understanding of the answer provided here.
Let us consider the first diagram. Here, we have a circle with center O. The radius of the circle is [tex] r [/tex]. Let the length of the arc be [tex] l [/tex] and it subtends an angle [tex] \theta [/tex] at the centre.
Now, we know that the relationship between arc length, [tex] l [/tex], radius, [tex] r [/tex] and angle subtended [tex] \theta [/tex] is given as:
[tex] l=r\times \theta=r \theta [/tex]
Thus, the relationship is linear and the graph between [tex] l [/tex] and [tex] \theta [/tex] for a given [tex] r [/tex] will be a straight line whose slope will be given by [tex] r [/tex].
Now, we also know that the maximum arc length that a circle can possibly have is the circumference of the circle which is given by [tex] 2\pi r [/tex] and that happens when the angle [tex] \theta [/tex] subtended at the center is equal to [tex] 2\pi [/tex].
Keeping the information of the above two paragraphs please have a look at the second diagram.
This second diagram is the required graph as asked in the question.
Answer:
Answer C for Plato
Step-by-step explanation:
Based on the explanation above
