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Arc Length & Area of a Sector — Easy Worksheet 2
Grade 10 · MathSheets Name: ____________________ Date: __________
Give answers in terms of π (like 6π) unless the problem says to use π ≈ 3.14; then round to the nearest tenth.
How to solve
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Example
Find the length of the highlighted arc. Leave your answer in terms of π.
Answer: 7π
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (90360) × 2π × 8 = (14) × 16π = 4π.
✓ Correct!
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (90360) × 2π × 8 = (14) × 16π = 4π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (180360) × π × 22 = (12) × 4π = 2π.
✓ Correct!
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (180360) × π × 22 = (12) × 4π = 2π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (180360) × 2π × 8 = (12) × 16π = 8π.
✓ Correct!
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (180360) × 2π × 8 = (12) × 16π = 8π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (270360) × π × 82 = (34) × 64π = 48π.
✓ Correct!
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (270360) × π × 82 = (34) × 64π = 48π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (180360) × 2π × 5 = (12) × 10π = 5π.
✓ Correct!
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (180360) × 2π × 5 = (12) × 10π = 5π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (180360) × π × 62 = (12) × 36π = 18π.
✓ Correct!
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (180360) × π × 62 = (12) × 36π = 18π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (270360) × 2π × 6 = (34) × 12π = 9π.
✓ Correct!
Not quite. The answer is
💡 Arc length = (θ/360) × 2πr = (270360) × 2π × 6 = (34) × 12π = 9π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (180360) × π × 42 = (12) × 16π = 8π.
✓ Correct!
Not quite. The answer is
💡 Sector area = (θ/360) × πr2 = (180360) × π × 42 = (12) × 16π = 8π.
💡 How to solve: Arc Length & Area of a Sector
A sector is a fraction of the circle: central angle ÷ 360°. Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr2. Simplify the fraction first, multiply, and keep π as a symbol unless told to use 3.14. To work backwards, set the formula equal to the given value and solve for θ or r.
Try a similar one
Find the length of the highlighted arc. Leave your answer in terms of π.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Arc Length & Area of a Sector — Easy Worksheet 2
Give answers in terms of π (like 6π) unless the problem says to use π ≈ 3.14; then round to the nearest tenth.