BMST Geometric Area and Volume 3 — Questions and Answers
Question 1: A sphere has a radius of 6 cm. What is its volume? (Use π ≈ 3.14)
- 904.32 cubic cm (Correct answer)
- 452.16 cubic cm
- 1,808.64 cubic cm
- 226.08 cubic cm
Correct answer: 904.32 cubic cm
Volume of a sphere = (4/3) × π × r³ = (4/3) × 3.14 × 216 = 904.32 cubic cm.
Question 2: A farmer wants to fence a rectangular field 120 yards long and 85 yards wide. What is the total area of the field?
- 10,200 square yards (Correct answer)
- 410 square yards
- 5,100 square yards
- 20,400 square yards
Correct answer: 10,200 square yards
Area = length × width = 120 × 85 = 10,200 square yards.
Question 3: A cone has a base radius of 4 inches and a height of 9 inches. What is its volume? (Use π ≈ 3.14)
- 150.72 cubic inches (Correct answer)
- 452.16 cubic inches
- 75.36 cubic inches
- 200.96 cubic inches
Correct answer: 150.72 cubic inches
Volume of a cone = (1/3) × π × r² × h = (1/3) × 3.14 × 16 × 9 = 150.72 cubic inches.
Question 4: The base of a right triangle is 9 meters and the hypotenuse is 15 meters. What is the area of the triangle?
- 54 square meters (Correct answer)
- 67.5 square meters
- 108 square meters
- 45 square meters
Correct answer: 54 square meters
Using the Pythagorean theorem, height = √(15² - 9²) = √144 = 12 m; Area = ½ × 9 × 12 = 54 square meters.
Question 5: A square tile has a side of 9 inches. How many tiles are needed to cover a floor area of 3,645 square inches?
- 45 tiles (Correct answer)
- 81 tiles
- 405 tiles
- 36 tiles
Correct answer: 45 tiles
Area of one tile = 9² = 81 square inches; Number of tiles = 3,645 ÷ 81 = 45 tiles.
Question 6: A rectangular prism has a length of 10 m, width of 4 m, and height of 3 m. What is the total surface area?
- 164 square meters (Correct answer)
- 120 square meters
- 328 square meters
- 82 square meters
Correct answer: 164 square meters
SA = 2(lw + lh + wh) = 2(40 + 30 + 12) = 2 × 82 = 164 square meters.
Question 7: A circular fountain has a circumference of 31.4 feet. What is the area of its surface? (Use π ≈ 3.14)
- 78.5 square feet (Correct answer)
- 31.4 square feet
- 314 square feet
- 157 square feet
Correct answer: 78.5 square feet
C = 2πr → r = 31.4 ÷ (2 × 3.14) = 5 ft; Area = π × 5² = 3.14 × 25 = 78.5 square feet.
BMST Geometric Area and Volume 3
A sphere has a radius of 6 cm.
What is its volume? (Use π ≈ 3.14)