Arc Length on a Circle Practice Test

Arc Length on a Circle Practice Test:

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#1:

Instructions: Find the length of each arc.

$$a)\hspace{.1em}r=10 \hspace{.15em}\text{mi}, θ=\frac{7π}{12}$$

$$b)\hspace{.1em}r=10 \hspace{.15em}\text{km}, θ=\frac{5π}{6}$$

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#2:

Instructions: Find the length of each arc.

$$a)\hspace{.1em}r=6 \hspace{.15em}\text{cm}, θ=\frac{17π}{12}$$

$$b)\hspace{.1em}r=5 \hspace{.15em}\text{km}, θ=240°$$

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#3:

Instructions: Find the length of each arc.

$$a)\hspace{.1em}r=8 \hspace{.15em}\text{m}, θ=120°$$

$$b)\hspace{.1em}r=19 \hspace{.15em}\text{cm}, θ=270°$$

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#4:

Instructions: Find the area of each sector.

$$a)\hspace{.1em}r=9 \hspace{.15em}\text{yd}, θ=\frac{7π}{6}$$

$$b)\hspace{.1em}r=16 \hspace{.15em}\text{ft}, θ=\frac{3π}{2}$$

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#5:

Instructions: Find the area of each sector.

$$a)\hspace{.1em}r=8 \hspace{.15em}\text{cm}, θ=90°$$

$$b) \hspace{.1em}r=12 \hspace{.15em}\text{yd}, θ=270°$$

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Written Solutions:

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#1:

Solutions:

$$a)\hspace{.1em}\frac{35π}{6}\hspace{.1em}\text{mi}$$

$$b)\hspace{.1em}\frac{25π}{3}\hspace{.1em}\text{km}$$

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#2:

Solutions:

$$a)\hspace{.1em}\frac{17π}{2}\hspace{.1em}\text{cm}$$

$$b)\hspace{.1em}\frac{20π}{3}\hspace{.1em}\text{km}$$

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#3:

Solutions:

$$a)\hspace{.1em}\frac{16π}{3}\hspace{.1em}\text{m}$$

$$b)\hspace{.1em}\frac{57π}{2}\hspace{.1em}\text{cm}$$

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#4:

Solutions:

$$a)\hspace{.1em}\frac{189π}{4}\hspace{.1em}\text{yd}^2$$

$$b)\hspace{.1em}192π \hspace{.1em}\text{ft}^2$$

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#5:

Solutions:

$$a)\hspace{.1em}16π \hspace{.1em}\text{cm}^2$$

$$b)\hspace{.1em}108π \hspace{.1em}\text{yd}^2$$

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