Area of a Circle Sector From Area to Angle (Equation) (Level 3)

This math topic focuses on determining the sector angle of a circle given the sector's area and the circle's radius. It is nested within a broader unit on circle geometry, specifically covering areas of circle sectors and related aspects. Through a series of questions, learners are tasked with calculating the angle of a circle sector based on provided areas and radius values, applying the formula \( \theta = \frac{{360 \times (sector\ area)}}{{\pi \times radius^2}} \). Each question presents multiple-choice answers, encouraging hands-on problem-solving within the theme of circle geometry.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Area of a Circle Sector From Area to Angle (Equation) Worksheet

Math worksheet on 'Area of a Circle Sector From Area to Angle (Equation) (Level 3)'. Part of a broader unit on 'Geometry - Circle Area, Sectors and Donuts - Intro' Learn online: app.mobius.academy/math/units/geometry_circles_sector_donut_area_logic_intro/

1

Find the sector angle for a sector with area 3 π in a circle of radius 3

a

240º

b

480º

c

60º

d

120º

e

600º

f

300º

2

Find the sector angle for a sector with area 3/2 π in a circle of radius 3

a

300º

b

240º

c

90º

d

30º

e

120º

f

60º

3

Find the sector angle for a sector with area 5 π in a circle of radius 5

a

2º

b

177º

c

72º

d

173º

e

208º

f

212º

4

Find the sector angle for a sector with area 36/5 π in a circle of radius 3

a

132º

b

272º

c

1,408º

d

288º

e

428º

f

1,128º

5

Find the sector angle for a sector with area 25/3 π in a circle of radius 5

a

240º

b

480º

c

120º

d

300º

e

360º

f

540º

6

Find the sector angle for a sector with area 24 π in a circle of radius 6

a

840º

b

120º

c

960º

d

600º

e

240º

f

480º

7

Find the sector angle for a sector with area 32/9 π in a circle of radius 4

a

280º

b

200º

c

360º

d

80º

e

160º

f

320º