Circle, Arcs and Sectors (Copy)

Q1 (Non-Calculator)
Find the circumference of a circle with radius 7 cm. Leave your answer in terms of π.

Solution:
Circumference = 2πr
Circumference = 2π × 7
Circumference = 14π cm

Answer:
14π cm

Q2 (Non-Calculator)
Find the area of a circle with radius 5 cm. Give your answer in terms of π.

Solution:
Area = πr²
Area = π × 5²
Area = π × 25
Area = 25π cm²

Answer:
25π cm²

Q3 (Non-Calculator)
Find the circumference of a circle with diameter 12 cm. Leave your answer in terms of π.

Solution:
Circumference = πd
Circumference = π × 12
Circumference = 12π cm

Answer:
12π cm

Q4 (Non-Calculator)
Find the area of a circle with diameter 10 cm. Leave your answer in terms of π.

Solution:
Radius = 10 ÷ 2 = 5 cm
Area = πr²
Area = π × 5²
Area = π × 25
Area = 25π cm²

Answer:
25π cm²

Q5 (Non-Calculator)
Find the length of an arc of a circle with radius 6 cm and sector angle 90°. Give your answer in terms of π.

Solution:
Arc Length = (θ ÷ 360) × 2πr
Arc Length = (90 ÷ 360) × 2π × 6
Arc Length = (1/4) × 12π
Arc Length = 3π cm

Answer:
3π cm

Q6 (Calculator)
Find the area of a sector with radius 8 cm and angle 60°. Give your answer in terms of π.

Solution:
Sector Area = (θ ÷ 360) × πr²
Sector Area = (60 ÷ 360) × π × 8²
Sector Area = (1/6) × π × 64
Sector Area = (64 ÷ 6)π
Sector Area = (32 ÷ 3)π cm²

Answer:
(32/3)π cm²

Q7 (Calculator)
Find the arc length of a sector with radius 10 cm and sector angle 120°. Give your answer in terms of π.

Solution:
Arc Length = (θ ÷ 360) × 2πr
Arc Length = (120 ÷ 360) × 2π × 10
Arc Length = (1/3) × 20π
Arc Length = (20/3)π cm

Answer:
(20/3)π cm

Q8 (Calculator)
Find the area of a semicircle with radius 9 cm. Give your answer in terms of π.

Solution:
Area of full circle = πr² = π × 9² = 81π
Area of semicircle = (1/2) × 81π
Area = 40.5π cm²

Answer:
40.5π cm²

Q9 (Calculator)
Find the length of an arc in a circle of radius 5 cm, subtended by an angle of 180°. Give your answer in terms of π.

Solution:
Arc Length = (θ ÷ 360) × 2πr
Arc Length = (180 ÷ 360) × 2π × 5
Arc Length = (1/2) × 10π
Arc Length = 5π cm

Answer:
5π cm

Q10 (Calculator)
Find the area of a quarter-circle with radius 12 cm. Give your answer in terms of π.

Solution:
Area of full circle = πr² = π × 12² = 144π
Area of quarter circle = (1/4) × 144π
Area = 36π cm²

Answer:
36π cm²