West B Test Math: Geometry and Measurement 5 — Questions and Answers
Question 1: A right circular cone has a radius of 5 cm and a slant height of 13 cm. What is its lateral surface area? (Use π ≈ 3.14)
- 65 cm²
- 102.4 cm²
- 204.1 cm² (Correct answer)
- 408.2 cm²
Correct answer: 204.1 cm²
Lateral surface area = πrl = 3.14 × 5 × 13 = 204.1 cm².
Question 2: What is the midpoint of the segment connecting (−3, 4) and (7, −2)?
- (2, 1) (Correct answer)
- (2, 2)
- (5, 1)
- (4, 2)
Correct answer: (2, 1)
Midpoint = ((−3+7)/2, (4+(−2))/2) = (4/2, 2/2) = (2, 1).
Question 3: A square has a diagonal of 10 cm. What is the area of the square?
- 25 cm²
- 50 cm² (Correct answer)
- 70.7 cm²
- 100 cm²
Correct answer: 50 cm²
For a square with diagonal d, area = d²/2 = 10²/2 = 100/2 = 50 cm².
Question 4: Which of the following pairs of triangles CANNOT be proven congruent using the SAS (Side-Angle-Side) postulate?
- Two sides and the included angle are equal
- Two sides and a non-included angle are equal (Correct answer)
- Two sides and the angle between them are equal
- The two legs and the vertex angle are equal in isosceles triangles
Correct answer: Two sides and a non-included angle are equal
SAS requires the angle to be between (included by) the two sides; two sides and a non-included angle describes SSA, which does not guarantee congruence.
Question 5: A sphere has a radius of 6 cm. What is its volume? (Use π ≈ 3.14)
- 150.72 cm³
- 301.44 cm³
- 904.32 cm³ (Correct answer)
- 1808.64 cm³
Correct answer: 904.32 cm³
Volume = (4/3)πr³ = (4/3) × 3.14 × 216 = 4.19 × 216 ≈ 904.32 cm³.
Question 6: In a coordinate plane, line m passes through (0, 3) and (4, 7). What is the slope of a line perpendicular to m?
- 1
- −1 (Correct answer)
- 4
- −4
Correct answer: −1
Slope of m = (7−3)/(4−0) = 1; perpendicular slope = −1/1 = −1.
Question 7: A right triangle has legs of 9 cm and 12 cm. What is the length of the hypotenuse?
- 13 cm
- 15 cm (Correct answer)
- 18 cm
- 21 cm
Correct answer: 15 cm
Hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.
West B Test Math: Geometry and Measurement 5
A right circular cone has a radius of 5 cm and a slant height of 13 cm.
What is its lateral surface area? (Use π ≈ 3.14)