TMUA Geometry & Measurement Concepts 2 — Questions and Answers
Question 1: A sector of a circle has radius 6 cm and central angle 120°. What is the area of the sector?
- 12π cm² (Correct answer)
- 6π cm²
- 18π cm²
- 24π cm²
Correct answer: 12π cm²
Area of sector = (θ/360°)·πr² = (120/360)·π·36 = 12π cm².
Question 2: Two circles have radii in the ratio 3:5. What is the ratio of their areas?
- 9:25 (Correct answer)
- 3:5
- 6:10
- 27:125
Correct answer: 9:25
Area scales with the square of radius, so the ratio is 3²:5² = 9:25.
Question 3: In triangle ABC, angle A = 90°, AB = 5, AC = 12. What is the length of the altitude from A to BC?
- 60/13 (Correct answer)
- 5·12/13
- 13/2
- 5/12
Correct answer: 60/13
BC = 13 (Pythagorean theorem); altitude h = (AB·AC)/BC = 60/13.
Question 4: A cylinder has radius r and height 2r. If the radius is doubled and height halved, what happens to the volume?
- It doubles (Correct answer)
- It quadruples
- It stays the same
- It is halved
Correct answer: It doubles
Original V = π r²·2r = 2πr³; new V = π(2r)²·r = 4πr³, which is twice the original.
Question 5: The diagonals of a rhombus are 10 cm and 24 cm. What is the perimeter of the rhombus?
- 52 cm (Correct answer)
- 48 cm
- 60 cm
- 56 cm
Correct answer: 52 cm
Each side = √(5²+12²) = 13 cm; perimeter = 4×13 = 52 cm.
Question 6: A sphere has surface area 100π cm². What is its volume?
- (500π/3) cm³ (Correct answer)
- 250π cm³
- 100π cm³
- (250π/3) cm³
Correct answer: (500π/3) cm³
4πr² = 100π → r = 5; V = (4/3)π(125) = 500π/3 cm³.
Question 7: Points A(1,2), B(5,2), and C(5,8) form a right triangle. What is the area of the circumscribed circle?
- (25π/2) units² (Correct answer)
- 25π units²
- (13π/2) units²
- 52π units²
Correct answer: (25π/2) units²
Hypotenuse AC has midpoint (3,5) and length √(16+36)=√52; circumradius = √52/2, area = π·52/4 = 13π.
TMUA Geometry & Measurement Concepts 2
A sector of a circle has radius 6 cm and central angle 120°.
What is the area of the sector?