Solution
- We are asked questions regarding the radii and circumference of the concentric circles.
- Thus, we should try to find the values of the radii and circumferences of the circles.
- The relevant formulas we will use are:
[tex]\begin{gathered} Circumference\text{ of an Arc:} \\ \frac{\theta}{360}\times2\pi r \\ \\ \text{Circumference of a Circle} \\ 2\pi r \end{gathered}[/tex]
The Radii:
- We can get the radii using the formula for the circumference of an arc given above.
[tex]\begin{gathered} \text{Smaller circle:} \\ \theta=30 \\ \frac{\theta}{360}\times2\pi r=3\pi \\ \\ \frac{30}{360}\times2\pi r=3\pi \\ \\ \frac{\pi r}{6}=3\pi \\ \\ r=6\times3=18 \\ \text{The radius of the smaller circle is 18}cm \\ \\ \\ \text{Larger Circle:} \\ \theta=30 \\ \frac{30}{360}\times2\pi r=6\pi \\ \\ \frac{\pi r}{6}=6\pi \\ \\ r=6\times6=36 \\ \text{The radius of the larger circle is 36}cm \end{gathered}[/tex]
The Circumferences:
- The circumferences of both circles are:
[tex]\begin{gathered} Smaller\text{ circle:} \\ 2\times\pi\times r=2\times\pi\times18=36\pi \\ \\ \text{Larger circle:} \\ 2\times\pi\times r=2\times\pi\times36=72\pi \end{gathered}[/tex]
With these values, we can proceed to eliminate options.
Option 1:
This is WRONG because the radius of the Larger circle is 36cm, not 18cm
Option 2:
This is CORRECT because the radius of the smaller circle is 18cm
Option 3:
The length of segment NE is the difference in both radii which is 36cm - 18cm = 18cm. This is not equal to 9cm. Thus, this option is WRONG
Option 4:
This option is CORRECT because MR is also a difference in both radii and it is 18cm
Option 5:
This is CORRECT because the circumference of the larger circle is 72 pi
Option 6:
This is WRONG
Final Answer
The answers are:
Option 2
Option 4
Option 5
