Find the Arc Length & Sector Area
Use 3.14 for π. Round answers to 2 decimal places.
Sector & Arc Challenge!
Find the area and arc length of circle sectors.
Sector & Arc Game
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This Sector & Arc Game is a great way to put your skills to the test in a fun environment. By practicing, you’ll start to work out the answers efficiently.
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Sector & Arc Game
An arc is just a portion of the circle’s circumference, and a sector is the wedge-shaped area of the circle enclosed by two radii and the arc. The formulas for arc length and area of a sector are directly related to the fraction of the whole circle you’re dealing with. Scroll down the page for a more detailed explanation.
In this game, you will be given the radius and the angle. Approximate π to 3.14 and round answers to two decimal places. If you give a wrong answer, the game will provide the correct answer.
Circumference of a Circle
Area of a Circle
Score: 0 / 0
How to Play the Sector & Arc Game
In the game, you need to find the arc length and the sector area given a radius and an angle.
Here’s how to play:
- Start Game: Click “Start Game”
- Find the Sector & Arc: You will be given the radius and angle of the sector. Find the arc length and sector area.
- Enter Your Answer: Enter in the answer. Approximate π by 3.14 and round answers to two decimal places.
- Check Your Work: Click the “Check” button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
- Get a New Problem: Click the “Next” button for a new problem.
Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried. - Back to Menu Click “Menu” to restart the game.
How to Find the Sector & Arc
An arc is a portion of the circle’s circumference, and a sector is the wedge-shaped area of the circle enclosed by two radii and the arc.
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Finding the Arc Length (L)
The arc length is essentially a fractional part of the circle’s Circumference (C = 2πr).
Using Degrees (θ in degrees)
When the central angle (θ) is in degrees, you compare it to the total degrees in a circle (360°).
Arc Length (L) = \(\frac{\text{Central Angle}}{360^\circ} \times \text{Circumference}\)
L = \(\frac{\theta}{360} \cdot 2\pi r\)
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Finding the Area of a Sector (A)
The area of a sector is a fractional part of the circle’s total Area \((A_{circle} = \pi r^2)\).
Using Degrees (θ in degrees)
When the central angle (θ) is in degrees, you use the same fraction comparison against 360°.
Sector Area (A) = \(\frac{\text{Central Angle}}{360^\circ} \times \text{Circle Area}\)
\(A = \frac{\theta}{360} \cdot \pi r^2\)
The video gives a clear, step-by-step approach to calculate the arc length and area of sector.
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