Bluebook SAT Test Area and Volume 6 — Questions and Answers
Question 1: A cylindrical can has diameter 10 cm and height 15 cm. What is the volume? (Leave in terms of π)
- 150π cm³
- 375π cm³ (Correct answer)
- 750π cm³
- 1500π cm³
Correct answer: 375π cm³
Radius = 5; V = π(5²)(15) = 375π cm³.
Question 2: A trapezoid has area 90 cm², height 9 cm, and one parallel side 8 cm. What is the other parallel side?
- 6 cm
- 10 cm
- 12 cm (Correct answer)
- 20 cm
Correct answer: 12 cm
90 = ½(8 + b₂)(9) → 20 = 8 + b₂ → b₂ = 12 cm.
Question 3: A composite figure is a 10 m × 10 m square with a triangle of base 10 m and height 6 m on top. What is the total area?
- 100 m²
- 130 m² (Correct answer)
- 160 m²
- 200 m²
Correct answer: 130 m²
Square = 100 m²; triangle = ½ × 10 × 6 = 30 m²; total = 130 m².
Question 4: A hemisphere (half-sphere) has radius 6 cm. What is its volume in terms of π?
- 72π cm³
- 144π cm³ (Correct answer)
- 216π cm³
- 432π cm³
Correct answer: 144π cm³
Full sphere = (4/3)π(6³) = (4/3)π(216) = 288π; hemisphere = 144π cm³.
Question 5: If the radius of a circle is increased by 50%, by what percent does the area increase?
- 50%
- 75%
- 100%
- 125% (Correct answer)
Correct answer: 125%
New area = π(1.5r)² = 2.25πr²; percent increase = (2.25 − 1) × 100% = 125%.
Question 6: A rectangular sandbox is 2 m × 3 m, filled with sand to a depth of 0.5 m. What is the volume of sand?
- 1 m³
- 3 m³ (Correct answer)
- 6 m³
- 12 m³
Correct answer: 3 m³
V = 2 × 3 × 0.5 = 3 m³.
Question 7: A triangle has base 18 cm and area 108 cm². What is the height?
- 6 cm
- 9 cm
- 12 cm (Correct answer)
- 18 cm
Correct answer: 12 cm
108 = ½ × 18 × h → h = 216/18 = 12 cm.
Bluebook SAT Test Area and Volume 6
A cylindrical can has diameter 10 cm and height 15 cm.
What is the volume? (Leave in terms of π)