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Two concentric circles are shown. The length of the arc MN is 37 cm and the length of the arc RE is 6 cm.Which statements are correct? Select all that apply.The radius of the larger circle is 18 cm.The radius of the smaller circle is 18 cm.The length of the segment NE is 9 cm.The length of the segment MR is 18 cmThe circumference of the larger circle is 72 cm.The circumference of the larger circle is 367 cmMacBook

Two Concentric Circles Are Shown The Length Of The Arc MN Is 37 Cm And The Length Of The Arc RE Is 6 CmWhich Statements Are Correct Select All That ApplyThe Rad class=

Sagot :

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

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