OAR OAR Math Skills: Geometry 5 — Questions and Answers
Question 1: A sphere has a radius of 3 in. What is its volume? (Use π ≈ 3.14)
- 113.04 in³ (Correct answer)
- 37.68 in³
- 452.16 in³
- 75.36 in³
Correct answer: 113.04 in³
V = (4/3) × π × r³ = (4/3) × 3.14 × 27 = 113.04 in³.
Question 2: Two similar triangles have corresponding sides in a ratio of 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?
- 75 cm² (Correct answer)
- 45 cm²
- 135 cm²
- 50 cm²
Correct answer: 75 cm²
The area ratio equals the square of the side ratio: (3/5)² = 9/25; larger area = 27 × (25/9) = 75 cm².
Question 3: A sector of a circle has a central angle of 90° and radius 8 cm. What is the area of the sector? (Use π ≈ 3.14)
- 50.24 cm² (Correct answer)
- 25.12 cm²
- 200.96 cm²
- 100.48 cm²
Correct answer: 50.24 cm²
Area = (θ/360°) × πr² = (90/360) × 3.14 × 64 = 0.25 × 200.96 = 50.24 cm².
Question 4: A line passes through points (0, 4) and (3, 10). What is the equation of the line?
- y = 2x + 4 (Correct answer)
- y = 3x + 4
- y = 2x + 6
- y = x + 4
Correct answer: y = 2x + 4
Slope = (10 − 4)/(3 − 0) = 6/3 = 2; y-intercept = 4; equation: y = 2x + 4.
Question 5: Which transformation maps a figure onto itself only if the figure has rotational symmetry?
- Rotation (Correct answer)
- Reflection
- Translation
- Dilation
Correct answer: Rotation
A rotation maps a figure onto itself only when the figure has rotational symmetry about the center of rotation.
Question 6: A right circular cylinder has a volume of 502.4 cm³ and height of 10 cm. What is its radius? (Use π ≈ 3.14)
- 4 cm (Correct answer)
- 5 cm
- 8 cm
- 2 cm
Correct answer: 4 cm
V = πr²h → r² = 502.4 ÷ (3.14 × 10) = 502.4 ÷ 31.4 = 16; r = 4 cm.
Question 7: In triangle PQR, PQ = QR = 10 and PR = 12. What is the height from Q to PR?
- 8 (Correct answer)
- 6
- 5
- 10
Correct answer: 8
The height bisects PR at 6; using Pythagoras: h = √(10² − 6²) = √(100 − 36) = √64 = 8.
OAR OAR Math Skills: Geometry 5
A sphere has a radius of 3 in.
What is its volume? (Use π ≈ 3.14)