College Math Placement Test Geometry 3 — Questions and Answers
Question 1: A sector of a circle has a central angle of 90° and radius 8. What is the area of the sector?
- 16π (Correct answer)
- 64π
- 32π
- 8π
Correct answer: 16π
Area = (90/360)πr² = (1/4)π(64) = 16π.
Question 2: Triangle DEF is similar to triangle GHI with a scale factor of 3:5. If DE = 12, what is GH?
- 20 (Correct answer)
- 36
- 7.2
- 15
Correct answer: 20
12/GH = 3/5, so GH = 12 × 5/3 = 20.
Question 3: What is the volume of a cylinder with radius 3 and height 10?
- 90π (Correct answer)
- 30π
- 60π
- 180π
Correct answer: 90π
Volume = πr²h = π(9)(10) = 90π.
Question 4: A quadrilateral has interior angles of 85°, 95°, 110°, and x°. What is x?
- 70 (Correct answer)
- 80
- 90
- 60
Correct answer: 70
Sum of interior angles of a quadrilateral is 360°; x = 360 − 85 − 95 − 110 = 70.
Question 5: Point M is the midpoint of segment AB. If A = (2, −4) and M = (5, 1), what are the coordinates of B?
- (8, 6) (Correct answer)
- (3.5, −1.5)
- (7, 2)
- (10, 3)
Correct answer: (8, 6)
B = (2(5) − 2, 2(1) − (−4)) = (8, 6).
Question 6: A rhombus has diagonals of length 10 and 24. What is the perimeter of the rhombus?
- 52 (Correct answer)
- 240
- 48
- 60
Correct answer: 52
Each side = √(5² + 12²) = √169 = 13; perimeter = 4 × 13 = 52.
Question 7: An isosceles right triangle has a hypotenuse of 10. What is the length of each leg?
- 5√2 (Correct answer)
- 5
- 10√2
- 10/√3
Correct answer: 5√2
For a 45-45-90 triangle, leg = hypotenuse/√2 = 10/√2 = 5√2.
College Math Placement Test Geometry 3
A sector of a circle has a central angle of 90° and radius 8.
What is the area of the sector?