Bluebook SAT Test Area and Volume 9 — Questions and Answers
Question 1: A rhombus has diagonals of length 10 cm and 16 cm. What is the area of the rhombus?
- 80 cm² (Correct answer)
- 160 cm²
- 40 cm²
- 50 cm²
Correct answer: 80 cm²
Area of a rhombus = (d₁ × d₂) / 2 = (10 × 16) / 2 = 80 cm².
Question 2: A rectangular swimming pool measures 15 m × 8 m and is uniformly 2 m deep. How many cubic meters of water does it hold?
- 240 m³ (Correct answer)
- 120 m³
- 46 m³
- 480 m³
Correct answer: 240 m³
Volume = length × width × depth = 15 × 8 × 2 = 240 m³.
Question 3: A circle is inscribed in a square with side length 6. What is the area of the region inside the square but outside the circle? (Use π ≈ 3.14)
- 7.74 (Correct answer)
- 36
- 28.26
- 11.46
Correct answer: 7.74
Square area = 36; circle area = π(3)² ≈ 28.26; difference = 36 − 28.26 = 7.74.
Question 4: A triangular prism has a right-triangle base with legs 5 cm and 12 cm. The prism's length is 9 cm. What is the volume?
- 270 cm³ (Correct answer)
- 540 cm³
- 135 cm³
- 60 cm³
Correct answer: 270 cm³
Base area = (1/2)(5)(12) = 30 cm²; volume = 30 × 9 = 270 cm³.
Question 5: A square piece of land has area 225 m². A path 1 m wide runs along the inside perimeter. What is the area of the path?
- 56 m² (Correct answer)
- 60 m²
- 44 m²
- 52 m²
Correct answer: 56 m²
Side = 15 m; inner square side = 13 m; inner area = 169 m²; path area = 225 − 169 = 56 m².
Question 6: A solid hemisphere has radius 6 cm. What is its total surface area in terms of π?
- 108π cm² (Correct answer)
- 72π cm²
- 144π cm²
- 36π cm²
Correct answer: 108π cm²
Total surface area = curved area + flat circle = 2πr² + πr² = 3πr² = 3π(36) = 108π cm².
Question 7: Two similar cones have radii in the ratio 2:3. The smaller cone has volume 16π cm³. What is the volume of the larger cone?
- 54π cm³ (Correct answer)
- 24π cm³
- 36π cm³
- 81π cm³
Correct answer: 54π cm³
Volume ratio = (2/3)³ = 8/27; larger volume = 16π × (27/8) = 54π cm³.
Bluebook SAT Test Area and Volume 9
A rhombus has diagonals of length 10 cm and 16 cm.
What is the area of the rhombus?