BMST Geometric Area and Volume 4 — Questions and Answers
Question 1: A room floor measures 15 feet by 12 feet. Carpet costs $3.50 per square foot. How much will it cost to carpet the entire floor?
- $630 (Correct answer)
- $94.50
- $189
- $378
Correct answer: $630
Area = 15 × 12 = 180 sq ft; Cost = 180 × $3.50 = $630.
Question 2: A cylindrical can has a diameter of 10 cm and a height of 15 cm. What is the lateral (side) surface area? (Use π ≈ 3.14)
- 471 square cm (Correct answer)
- 235.5 square cm
- 942 square cm
- 1,177.5 square cm
Correct answer: 471 square cm
Lateral SA = 2πrh = 2 × 3.14 × 5 × 15 = 471 square cm.
Question 3: Two identical triangles are cut from a rectangle measuring 10 cm × 6 cm. What area remains?
- 30 square cm (Correct answer)
- 60 square cm
- 15 square cm
- 45 square cm
Correct answer: 30 square cm
Rectangle area = 60 sq cm; two triangles that together equal the rectangle = 60 sq cm; remaining = 60 - 30 = 30 sq cm (one triangle's area).
Question 4: A pyramid has a square base with sides of 6 m and a height of 8 m. What is its volume?
- 96 cubic meters (Correct answer)
- 288 cubic meters
- 48 cubic meters
- 144 cubic meters
Correct answer: 96 cubic meters
Volume of a pyramid = (1/3) × base area × height = (1/3) × 36 × 8 = 96 cubic meters.
Question 5: A parallelogram has a base of 14 cm and a height of 7 cm. What is its area?
- 98 square cm (Correct answer)
- 49 square cm
- 196 square cm
- 147 square cm
Correct answer: 98 square cm
Area of a parallelogram = base × height = 14 × 7 = 98 square cm.
Question 6: A hollow pipe has an outer radius of 5 cm and an inner radius of 3 cm. What is the area of its circular cross-section? (Use π ≈ 3.14)
- 50.24 square cm (Correct answer)
- 78.5 square cm
- 28.26 square cm
- 100.48 square cm
Correct answer: 50.24 square cm
Area = π(R² - r²) = 3.14 × (25 - 9) = 3.14 × 16 = 50.24 square cm.
Question 7: A box without a lid is 8 inches long, 5 inches wide, and 4 inches tall. What is the total surface area of the box (5 sides only)?
- 144 square inches (Correct answer)
- 184 square inches
- 160 square inches
- 120 square inches
Correct answer: 144 square inches
Bottom = 8×5 = 40; two long sides = 2(8×4) = 64; two short sides = 2(5×4) = 40; Total = 40 + 64 + 40 = 144 square inches.
BMST Geometric Area and Volume 4
A room floor measures 15 feet by 12 feet.
Carpet costs $3.50 per square foot.
How much will it cost to carpet the entire floor?