Find the Arc Length & Sector Area
Round answers to 2 decimal places.
Sector & Arc (Radians)!
Find the area and arc length of circle sectors.
Arc & Sector (Radians) Game
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This Arc & Sector (Radians) 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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Arc & Sector (Radians) 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 in radians and asked to find the arc length and area of the sector. 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 Arc & Sector (Radians) Game
In the game, you need to find the arc length and the sector area given a radius and an angle in radians.
Here’s how to play:
- Start Game: Click “Start Game”
- Find the Arc & Sector (Radians): 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. 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 Arc & Sector (Radians)
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)
When the central angle (θ) is in radians, the formula is much simpler, which is why radians are often preferred in higher math.
Arc Length (L) = Radius × Central Angle (in radians)
L = rθ
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Finding the Area of a Sector (A)
When the central angle (θ) is in radians, the formula is:
Sector Area (A) = \(\frac{1}{2}\) × Radius2 × Central Angle (in radians)
\(A = \frac{1}{2} r^2 \theta\)
The video gives a clear, step-by-step approach to calculate the arc length and area of sector.
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