Bluebook SAT Test Area and Volume 8 — Questions and Answers
Question 1: A circular pool has radius 5 m. How much fencing (circumference) is needed? (Use π ≈ 3.14)
- 15.7 m
- 31.4 m (Correct answer)
- 62.8 m
- 78.5 m
Correct answer: 31.4 m
C = 2πr = 2 × 3.14 × 5 = 31.4 m.
Question 2: A right rectangular prism has length 8, width 5, and height 4. What is the total surface area?
- 104
- 164
- 184 (Correct answer)
- 320
Correct answer: 184
SA = 2(lw + lh + wh) = 2(40 + 32 + 20) = 2(92) = 184.
Question 3: A sector has central angle 90° and radius 8 cm. What is its area in terms of π?
- 4π cm²
- 8π cm²
- 16π cm² (Correct answer)
- 64π cm²
Correct answer: 16π cm²
Area = (90/360) × π(8²) = ¼ × 64π = 16π cm².
Question 4: A ring is formed by a circle of radius 4 m minus a circle of radius 2 m at its center. What is the ring's area in terms of π?
- 4π m²
- 8π m²
- 12π m² (Correct answer)
- 16π m²
Correct answer: 12π m²
Area = π(4²) − π(2²) = 16π − 4π = 12π m².
Question 5: A triangular prism has a cross-section with base 5 cm and height 6 cm, and is 12 cm long. What is its volume?
- 90 cm³
- 180 cm³ (Correct answer)
- 360 cm³
- 720 cm³
Correct answer: 180 cm³
V = (½ × 5 × 6) × 12 = 15 × 12 = 180 cm³.
Question 6: A circle's area equals the area of a square with side 10 cm. What is the approximate radius? (Use π ≈ 3.14)
- 3.19 cm
- 5.64 cm (Correct answer)
- 10 cm
- 17.8 cm
Correct answer: 5.64 cm
πr² = 100 → r² = 100/3.14 ≈ 31.85 → r ≈ 5.64 cm.
Question 7: A box has volume 360 cm³. If length and width are each doubled while height stays the same, what is the new volume?
- 720 cm³
- 1,080 cm³
- 1,440 cm³ (Correct answer)
- 2,880 cm³
Correct answer: 1,440 cm³
New V = (2l)(2w)(h) = 4lwh = 4 × 360 = 1,440 cm³.
Bluebook SAT Test Area and Volume 8
A circular pool has radius 5 m.
How much fencing (circumference) is needed? (Use π ≈ 3.14)