TMUA Geometry & Measurement Concepts 3 — Questions and Answers
Question 1: An arc of a circle subtends an angle of 2 radians at the center. If the arc length is 8 cm, what is the area of the sector?
- 16 cm² (Correct answer)
- 8 cm²
- 32 cm²
- 4 cm²
Correct answer: 16 cm²
Arc length s = rθ → r = 4 cm; sector area = ½r²θ = ½·16·2 = 16 cm².
Question 2: A regular hexagon has side length 4 cm. What is its area?
- 24√3 cm² (Correct answer)
- 48 cm²
- 12√3 cm²
- 96 cm²
Correct answer: 24√3 cm²
Area of regular hexagon = (3√3/2)s² = (3√3/2)·16 = 24√3 cm².
Question 3: Two parallel lines are cut by a transversal. One co-interior angle is 3x + 10° and the other is 2x + 20°. Find x.
- 30° (Correct answer)
- 26°
- 22°
- 34°
Correct answer: 30°
Co-interior (same-side interior) angles sum to 180°: 5x + 30 = 180 → x = 30°.
Question 4: A cone has base radius 3 cm and slant height 5 cm. What is its total surface area?
- 24π cm² (Correct answer)
- 15π cm²
- 9π cm²
- 18π cm²
Correct answer: 24π cm²
Total surface area = πrl + πr² = π·3·5 + π·9 = 15π + 9π = 24π cm².
Question 5: In a circle, a chord of length 16 cm is 6 cm from the center. What is the radius?
- 10 cm (Correct answer)
- 8 cm
- √(64+36) cm
- 14 cm
Correct answer: 10 cm
The perpendicular from center bisects the chord; r = √(8²+6²) = √100 = 10 cm.
Question 6: A square is inscribed in a circle of radius 5 cm. What is the area of the square?
- 50 cm² (Correct answer)
- 25 cm²
- 100 cm²
- 25√2 cm²
Correct answer: 50 cm²
The diagonal of the square equals the diameter = 10; side = 10/√2, area = 100/2 = 50 cm².
Question 7: The angle subtended by a chord at the center is 80°. What is the angle subtended by the same chord at any point on the major arc?
- 40° (Correct answer)
- 80°
- 100°
- 160°
Correct answer: 40°
The inscribed angle on the major arc is half the central angle: 80°/2 = 40°.
TMUA Geometry & Measurement Concepts 3
An arc of a circle subtends an angle of 2 radians at the center.
If the arc length is 8 cm, what is the area of the sector?