Circles, Arcs and Sector (Copy)
1.
A circle has radius 7 cm.
Find its circumference in terms of π.
2.
A circle has diameter 20 cm.
Find its circumference, giving your answer in terms of π.
3.
A circle has radius 14 cm.
Find its area in terms of π.
4.
A circular park has radius 21 m.
Find its area in m², giving your answer in terms of π.
5.
A circle has radius 6 cm.
Find the circumference correct to 2 decimal places (Ï€ = 3.142).
6.
The area of a circle is 154 cm².
Find its radius. (Take π = 3.142).
7.
A wheel has diameter 56 cm.
Find its circumference.
8.
A circular garden has circumference 88 m.
Find its radius. (Take π = 22/7).
9.
The radius of a circle is 8 cm.
Find the length of an arc subtending 90° at the centre.
10.
The radius of a circle is 10 cm.
Find the length of an arc subtending 120° at the centre, in terms of π.
11.
The radius of a circle is 12 cm.
Find the area of a sector that subtends 60° at the centre.
12.
The radius of a circle is 15 cm.
Find the area of a sector subtending 90° at the centre, in terms of π.
13.
The radius of a circle is 20 cm.
Find the length of the arc subtending 72° at the centre.
14.
The radius of a circle is 9 cm.
Find the area of the minor sector subtending 120°.
15.
A circle of radius 7 cm has a chord subtending 90° at the centre.
Find the arc length in terms of π.
16.
A circle has radius 25 cm.
Find the length of an arc subtending 54°.
17.
The radius of a circle is 18 cm.
Find the area of the major sector subtending 300°.
18.
A circle has radius 12 cm.
Find the length of the major arc subtending 270°.
19.
The radius of a circle is 14 cm.
Find the area of the minor sector subtending 45°.
20.
A circle has diameter 14 cm.
Find its circumference in terms of π.
21.
The radius of a circle is 9 cm.
Find its area, giving your answer in terms of π.
22.
A circle has radius 11 cm.
Find the area of a sector subtending 72° at the centre, in terms of π.
23.
The circumference of a circle is 132 cm.
Find its radius. (Use π = 22/7).
24.
The area of a circle is 616 cm².
Find its diameter. (Use π = 22/7).
25.
A sector of radius 5 cm subtends angle 144° at the centre.
Find its arc length.
26.
A sector of radius 8 cm subtends angle 150° at the centre.
Find its area in terms of π.
27.
A circle has radius 21 cm.
Find the length of the arc subtending angle 210° at the centre.
28.
The radius of a circle is 16 cm.
Find the area of the minor sector subtending angle 30°.
29.
A major sector of a circle has angle 300°. If radius = 10 cm,
find its area.
30.
The diameter of a circular pond is 28 m.
Find its circumference and area in terms of π.
1.
Circumference = 2πr = 2π×7 = 14π cm.
2.
Circumference = πd = π×20 = 20π cm.
3.
Area = πr² = π×14² = 196π cm².
4.
Area = πr² = π×21² = π×441 = 441π m².
5.
Circumference = 2πr = 2×3.142×6 = 37.70 cm.
6.
Area = πr² = 154.
r² = 154 ÷ 3.142 ≈ 49 → r = 7 cm.
7.
Circumference = πd = π×56 = 56π cm.
8.
C = 2Ï€r = 88.
Using π = 22/7 → 2×(22/7)×r = 88.
r = (88×7)/(44) = 14.
Radius = 14 m.
9.
Arc length = (θ/360)×2πr = (90/360)×2π×8 = (¼)×16π = 4π cm.
10.
Arc length = (120/360)×2π×10 = (⅓)×20π = 20/3 π cm.
11.
Sector area = (θ/360)×πr² = (60/360)×π×12² = (1/6)×144π = 24π cm².
12.
Sector area = (90/360)×π×15² = (¼)×225π = 56.25π cm².
13.
Arc length = (72/360)×2π×20 = (1/5)×40π = 8π cm.
14.
Sector area = (120/360)×π×9² = (⅓)×81π = 27π cm².
15.
Arc length = (90/360)×2π×7 = (¼)×14π = 3.5π cm.
16.
Arc length = (54/360)×2π×25 = (0.15)×50π = 7.5π cm.
17.
Sector area = (300/360)×π×18² = (5/6)×324π = 270π cm².
18.
Arc length = (270/360)×2π×12 = (¾)×24π = 18π cm.
19.
Sector area = (45/360)×π×14² = (⅛)×196π = 24.5π cm².
20.
Circumference = πd = π×14 = 14π cm.
21.
Area = πr² = π×9² = 81π cm².
22.
Sector area = (72/360)×π×11² = (⅕)×121π = 24.2π cm².
23.
C = 132 = 2Ï€r.
Using π=22/7 → 2×22/7×r=132 → r=(132×7)/44=21.
Radius = 21 cm.
24.
Area = 616 = πr².
Using π=22/7 → r²=616×7/22=196 → r=14.
Diameter = 28 cm.
25.
Arc length = (144/360)×2π×5 = (0.4)×10π = 4π cm.
26.
Sector area = (150/360)×π×8² = (5/12)×64π = 80/3 π cm².
27.
Arc length = (210/360)×2π×21 = (7/12)×42π = 24.5π cm.
28.
Sector area = (30/360)×π×16² = (1/12)×256π = 64/3 π cm².
29.
Sector area = (300/360)×π×10² = (5/6)×100π = 500/6 π ≈ 83.3π cm².
30.
Diameter = 28 → radius=14.
Circumference = 2Ï€r = 28Ï€ m.
Area = πr² = π×14² = 196π m².