10 questions · Form 5 Additional Mathematics Bab 1: Circular Measure
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. An arc of a circle of radius 8 cm subtends an angle of 1.25 rad at the centre. Calculate the length of the arc.
Answer: C
s = rθ = 8 × 1.25 = 10.0 cm.
2. If the arc length of a circle is equal to twice its radius, what is the central angle in radians?
Answer: D
s = rθ => 2r = rθ => θ = 2.0 rad.
3. A wheel rotates through 15 complete revolutions. What is the total angle rotated in radians?
Answer: B
1 revolution = 2π rad. 15 revolutions = 15 × 2π = 30π rad.
4. A sector of a circle has a radius of 6 cm and an area of 27 cm². Find the central angle subtended in radians.
Answer: A
Area A = 12 r² θ => 27 = 12 (6²) θ => 27 = 18θ => θ = 2718 = 1.5 rad.
5. Express 225° in radians in terms of π.
Answer: C
225° × (π180°) = 225180 π = 54 π rad.
6. Find the perimeter of a sector with a radius of 10 cm and a central angle of 0.8 rad.
Answer: B
Arc length s = rθ = 10 × 0.8 = 8 cm. Perimeter = s + 2r = 8 + 2(10) = 28 cm.
7. A sector has an area of 50 cm² and a radius of 10 cm. Find the arc length of the sector.
Answer: A
A = 12 r s => 50 = 12 (10) s => 50 = 5s => s = 10 cm.
8. A pendulum of length 45 cm swings through an angle of 0.2 rad. Find the distance traveled by the tip of the pendulum.
Answer: B
s = rθ = 45 × 0.2 = 9 cm.
9. The perimeter of a sector of a circle of radius r cm is 25 cm. If the angle at the centre is 1.5 rad, find the value of r.
Answer: D
Perimeter = rθ + 2r = r(θ + 2). 25 = r(1.5 + 2) => 25 = 3.5r => r = 253.5 = 7.14 cm.
10. An arc length of 15 cm subtends an angle of 1.5 rad at the centre of a circle. What is the radius of the circle?
Answer: A
s = rθ => 15 = r(1.5) => r = 151.5 = 10 cm.