Question

First drop down answer choices A. pi/4 B. pi/ 2 C. 4pi D. piSecond drop down answer choices A. pi/4 B. pi/ 2 C. 4pi D. piThird drop down answer choices A. Larger B. Smaller Forth drop down answer choices A. Larger B. Smaller

Answer 1

Let 'a' represent the ratio of the arc length to its radius.

Given for the first circle,

`\begin{gathered} \text{Arc length=4pi} \\ \text{Radius}=16\text{units} \end{gathered}`

Therefore,

`\begin{gathered} a_1=(4\pi)/(16)=(\pi)/(4) \\ \therefore a_1=(\pi)/(4) \end{gathered}`

Given for the second circle,

`\begin{gathered} \text{Arc length=}5\pi \\ \text{Radius}=5units \end{gathered}`

Therefore,

`\begin{gathered} a_2=(5\pi)/(5)=\pi \\ \therefore a_2=\pi \end{gathered}`

Hence,

`\begin{gathered} \pi>(\pi)/(4) \\ \therefore a_2>a_1 \end{gathered}`

Final answers

First drop down

`(\pi)/(4)\text{ (OPTION }A)`

Second drop down

`\pi\text{ (OPTION D)}`

Third drop down

`Larger\text{ (OPTION A)}`

Fourth drop down

`Larger\text{ (OPTION A)}`