10 questions · Form 5 Additional Mathematics Bab 1: Circular Measure
If the arc length of a circle is equal to twice its radius, what is the central angle in radians?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. 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.
2. 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.
3. 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.
4. 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.
5. Convert 120° into radians in terms of π.
Answer: B
120° × (π180°) = (120180)π = 23 π rad.
6. Express 225° in radians in terms of π.
Answer: C
225° × (π180°) = 225180 π = 54 π rad.
7. 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.
8. 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.
9. Convert 5π6 radians to degrees.
Answer: B
(5π6) × (180°/π) = 5 × 30° = 150°.
10. The minor arc AB of a circle with centre O and radius 7 cm has a length of 11 cm. Find the major angle AOB in radians. (Take π = 3.142)
Answer: A
Minor angle θ = sr = 117 = 1.571 rad. Major angle = 2π - 1.571 = 2(3.142) - 1.571 = 6.284 - 1.571 = 4.713 rad.