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Geometry

Circle Area and Sectors

Lesson

The interior of a circle is its area. A pie-slice piece — a sector — is a fraction of that area, scaled by the central angle.

Formulas

A=πr2A = \pi r^2
sector area=θ360∘⋅πr2\text{sector area} = \frac{\theta}{360^\circ} \cdot \pi r^2

Worked example

Sector of 60∘60^\circ in circle with r=6r = 6 (π≈3.14\pi \approx 3.14):

16⋅3.14⋅36=18.84\tfrac{1}{6} \cdot 3.14 \cdot 36 = 18.84

Use π≈3.14\pi \approx 3.14 for all problems in this topic.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Area, r=5 (π=3.14)\text{Area, } r = 5 \ (\pi = 3.14)

Problem 2

Area, r=10\text{Area, } r = 10

Problem 3

Sector 90∘,r=4\text{Sector } 90^\circ, r = 4

Problem 4

Semicircle area, r=6\text{Semicircle area, } r = 6

Practice

Standard problems matching the lesson.

Problem 5

Area, r=3\text{Area, } r = 3

Problem 6

Area, r=7\text{Area, } r = 7

Problem 7

Area, d=20\text{Area, } d = 20

Problem 8

Sector 60∘,r=6\text{Sector } 60^\circ, r = 6

Problem 9

Sector 120∘,r=3\text{Sector } 120^\circ, r = 3

Problem 10

Sector 270∘,r=2\text{Sector } 270^\circ, r = 2

Problem 11

Sector 45∘,r=8\text{Sector } 45^\circ, r = 8

Problem 12

Sector 30∘,r=6\text{Sector } 30^\circ, r = 6

Problem 13

Sector 180∘,r=10\text{Sector } 180^\circ, r = 10

Problem 14

Pizza slice 1/8 of pizza, r=8\text{Pizza slice 1/8 of pizza, } r = 8

Problem 15

Pool area, r=5\text{Pool area, } r = 5

Problem 16

Area, r=12\text{Area, } r = 12

Problem 17

Sector 90∘,r=10\text{Sector } 90^\circ, r = 10

Problem 18

Sector 36∘,r=10\text{Sector } 36^\circ, r = 10

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Area 314. Radius?\text{Area 314. Radius?}

Problem 20

Sector 90∘ area 50.24. Radius?\text{Sector } 90^\circ \text{ area 50.24. Radius?}

Problem 21

Pizza d=12, slice 1/4\text{Pizza } d = 12, \text{ slice 1/4}

Problem 22

Sector 60∘,r=9\text{Sector } 60^\circ, r = 9

Problem 23

Annulus, outer 10, inner 8\text{Annulus, outer 10, inner 8}

Problem 24

Sector 240∘,r=6\text{Sector } 240^\circ, r = 6

Problem 25

Semicircle area 100.48. Radius?\text{Semicircle area 100.48. Radius?}

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