Printable math worksheet for calculating the area of sectors using given radius and arc length.

It looks like you've uploaded an image of a worksheet titled "Finding Arcs of Sectors", which contains several problems involving calculating the length of arcs in circles or sectors. Since I can't view images directly, I’ll guide you through how to solve such problems and explain the general method.

However, since you mentioned the image includes specific questions (like "length of arc = ?"), let's assume it's similar to standard arc length problems. Here’s how to approach them:

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🔷 Arc Length Formula:

The length of an arc (\( L \)) in a circle is given by:

\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]

Where:
- \( \theta \) = central angle in degrees
- \( r \) = radius of the circle
- \( \pi \approx 3.14 \) or use \( \frac{22}{7} \)

Alternatively, if the angle is in radians:
\[
L = r\theta \quad (\text{with } \theta \text{ in radians})
\]

But most of these problems use degrees.

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✔ Step-by-step Solution Process:

Let’s suppose one of the problems shows a sector with:
- Radius = 8 cm
- Central angle = 60°

Then:
\[
L = \frac{60}{360} \times 2\pi \times 8 = \frac{1}{6} \times 16\pi = \frac{16\pi}{6} = \frac{8\pi}{3} \approx 8.38 \text{ cm}
\]

So, the arc length would be approximately 8.38 cm.

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📌 Common Problem Types on This Worksheet:

1. Given radius and angle → find arc length
2. Given arc length and radius → find angle
3. Given arc length and angle → find radius
4. Composite shapes (e.g., two arcs or shaded regions)

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🔍 Example Problems (Typical from Such Sheets):

#### Example 1:
- Radius = 5 cm
- Angle = 90°
- Find arc length.

\[
L = \frac{90}{360} \times 2\pi \times 5 = \frac{1}{4} \times 10\pi = 2.5\pi \approx 7.85 \text{ cm}
\]

✔ Answer: 7.85 cm

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#### Example 2:
- Radius = 10 cm
- Angle = 120°
- Find arc length.

\[
L = \frac{120}{360} \times 2\pi \times 10 = \frac{1}{3} \times 20\pi = \frac{20\pi}{3} \approx 20.94 \text{ cm}
\]

✔ Answer: 20.94 cm

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#### Example 3:
- Arc length = 12 cm
- Radius = 6 cm
- Find angle.

Use:
\[
L = \frac{\theta}{360} \times 2\pi r
\Rightarrow 12 = \frac{\theta}{360} \times 2\pi \times 6
\Rightarrow 12 = \frac{\theta}{360} \times 12\pi
\Rightarrow \frac{12}{12\pi} = \frac{\theta}{360}
\Rightarrow \frac{1}{\pi} = \frac{\theta}{360}
\Rightarrow \theta = \frac{360}{\pi} \approx 114.6^\circ
\]

✔ Answer: ≈114.6°

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💡 Tips:

- Always check units (cm, m, etc.)
- Use \( \pi \approx 3.14 \) unless told otherwise.
- Round appropriately (often to nearest tenth).
- For semicircles: angle = 180°, so arc length = \( \pi r \)
- For quarter-circles: angle = 90°, arc length = \( \frac{1}{2}\pi r \)

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🧩 Final Advice:

If you can describe one specific problem from the image (e.g., “a sector with radius 7 cm and angle 45°”), I can give you the exact solution.

Or, if you can list the values for each question (radius, angle, what’s missing), I’ll walk you through all of them step by step.

Let me know!