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Sector Area & Perimeter Quiz

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Sector Area & Perimeter Quiz

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Area & perimeter of a sector

Created by

Esther Vinodhini
Esther Vinodhini
India

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Sector Area & Perimeter Quiz
 

Sector Area & Perimeter QuizOnline version

Area & perimeter of a sector

by Esther Vinodhini
1

A sector has radius 5 cm and central angle 60°. What is its area? (use π≈3.14)

2

A sector with radius 7 cm and angle 90° has what arc length?

3

What is the perimeter of a sector with r=4 cm and θ=120°?

4

For a sector with r=6 cm and θ=180°, what is the area?

5

If r=3 cm and θ=45°, find the arc length.

6

A sector with r=8 cm and θ=30° has what area?

7

Find the perimeter of a sector: r=5 cm, θ=240°.

8

A sector with r=9 cm and θ=0° has area how much?

9

If r=10 cm and θ=360°, sector area equals?

10

What is the arc length of a sector with r=2 cm and θ=270°?

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Area = (60/360)×π×r² = (1/6)×3.14×25 = 13.09 cm². If π≈3.14, correct area ≈ 13.1 cm².

Arc length for a 90° sector is (90/360)×2πr = (1/4)×2π×7 ≈ 11.0 cm; using the given formula θ/360×2πr gives 0.25×2×3.14×7 ≈ 11.0 cm.

Perimeter = two radii plus arc length. Arc = (θ/360)×2πr = (120/360)×2π×4 = (1/3)×8π = 8π/3 ≈ 8.38 cm; total ≈ 16.38 cm.

Half-circle sector: area = 0.5×π×r² = 0.5×π×36 = 18π ≈ 56.55 cm².

Arc length = θ/360 × 2πr. Here = 0.125×6π ≈ 2.36 cm.

Area = (θ/360)πr². 30/360=1/12; 1/12×64π ≈ 16.76 cm².

Arc length = (240/360)×2πr = (2/3)×2π×5 = 20π/3 ≈ 20.94 cm; total ≈ 31.42 cm.

Zero angle yields zero sector area regardless of radius.

Full circle is θ=360°, area is πr².

Arc length = θ/360 × 2πr; 270/360 = 3/4, so 3/4×4π = 3π ≈ 9.42 cm.

 
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