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. 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.
2. Convert 0.75 rad into degrees, giving your answer to two decimal places. (Take π = 3.142)
Answer: C
0.75 rad × (180° / 3.142) = 1353.142 = 42.97°.
3. In a circle with centre O and radius 8 cm, triangle OAB is formed where OA = OB = 8 cm and angle AOB = 0.9 rad. What is the area of triangle OAB? (Take sin(0.9 rad) = 0.7833)
Answer: A
Area of triangle = 12 ab sin C = 12 (8)(8) sin(0.9 rad) = 32 × 0.7833 = 25.07 cm².
4. The area of a circle is 100π cm². Calculate the area of a sector in this circle with a central angle of 0.5 rad.
Answer: C
Area of circle = π r² = 100π => r = 10 cm. Area of sector = 12 r² θ = 12 (10²) (0.5) = 25 cm².
5. 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.
6. 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.
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. Convert 5π6 radians to degrees.
Answer: B
(5π6) × (180°/π) = 5 × 30° = 150°.
9. Express 225° in radians in terms of π.
Answer: C
225° × (π180°) = 225180 π = 54 π rad.
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.