OAR OAR Math Skills: Geometry 4 — Questions and Answers
Question 1: The volume of a cube is 125 in³. What is the length of one edge?
- 5 in (Correct answer)
- 25 in
- 15.6 in
- 41.7 in
Correct answer: 5 in
V = s³ → s = ∛125 = 5 in.
Question 2: A right triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg?
- 12 (Correct answer)
- 8
- √194
- 18
Correct answer: 12
b² = 13² − 5² = 169 − 25 = 144; b = 12 (the 5-12-13 Pythagorean triple).
Question 3: An exterior angle of a triangle measures 110°. If one non-adjacent interior angle is 45°, what is the other non-adjacent interior angle?
- 65° (Correct answer)
- 70°
- 45°
- 35°
Correct answer: 65°
An exterior angle equals the sum of the two non-adjacent interior angles: 110° − 45° = 65°.
Question 4: What is the midpoint of the segment connecting (−4, 2) and (6, −8)?
- (1, −3) (Correct answer)
- (−1, 3)
- (2, −6)
- (5, 5)
Correct answer: (1, −3)
Midpoint = ((−4+6)/2, (2+(−8))/2) = (2/2, −6/2) = (1, −3).
Question 5: A cone has a radius of 6 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)
- 339.12 cm³ (Correct answer)
- 1017.36 cm³
- 226.08 cm³
- 678.24 cm³
Correct answer: 339.12 cm³
V = (1/3) × π × r² × h = (1/3) × 3.14 × 36 × 9 = 339.12 cm³.
Question 6: In a coordinate plane, line m has a slope of 3/4. What is the slope of a line perpendicular to m?
- −4/3 (Correct answer)
- 4/3
- 3/4
- −3/4
Correct answer: −4/3
Perpendicular slopes are negative reciprocals; the negative reciprocal of 3/4 is −4/3.
Question 7: A regular hexagon has a side length of 6 cm. What is the sum of its interior angles?
- 720° (Correct answer)
- 540°
- 1080°
- 360°
Correct answer: 720°
Sum of interior angles = (n − 2) × 180° = (6 − 2) × 180° = 720°.
OAR OAR Math Skills: Geometry 4
The volume of a cube is 125 in³.
What is the length of one edge?