Bluebook SAT Test Area and Volume 10 — Questions and Answers
Question 1: An equilateral triangle has side length 8. What is its area? (Leave answer in simplified radical form.)
- 16√3 (Correct answer)
- 32√3
- 64√3
- 8√3
Correct answer: 16√3
Area = (√3/4)s² = (√3/4)(64) = 16√3.
Question 2: A cylinder has radius 3 and height h. If the volume is 54π, what is h?
- 6 (Correct answer)
- 9
- 3
- 18
Correct answer: 6
V = πr²h → 54π = π(9)h → h = 54/9 = 6.
Question 3: A trapezoid has parallel sides of 7 ft and 13 ft. If its area is 100 ft², what is its height?
- 10 ft (Correct answer)
- 8 ft
- 12 ft
- 5 ft
Correct answer: 10 ft
A = ½(b₁ + b₂)h → 100 = ½(20)h = 10h → h = 10.
Question 4: A rectangular prism has surface area 94 cm². Its length is 5 cm and width is 4 cm. What is its height?
- 3 cm (Correct answer)
- 4 cm
- 5 cm
- 2 cm
Correct answer: 3 cm
SA = 2(lw + lh + wh) → 94 = 2(20 + 5h + 4h) → 47 = 20 + 9h → h = 3.
Question 5: A sector of a circle has radius 10 and central angle 72°. What is its arc length? (Leave in terms of π.)
- 4π (Correct answer)
- 20π
- 2π
- 8π
Correct answer: 4π
Arc length = (72/360)(2π)(10) = (1/5)(20π) = 4π.
Question 6: A glass has the shape of a cylinder with radius 4 cm and height 12 cm. It is 3/4 full of juice. What is the volume of juice? (Leave in terms of π.)
- 144π cm³ (Correct answer)
- 192π cm³
- 48π cm³
- 96π cm³
Correct answer: 144π cm³
Full volume = π(16)(12) = 192π; 3/4 × 192π = 144π cm³.
Question 7: A hollow cube has an outer edge of 8 cm and a wall thickness of 1 cm everywhere. What is the volume of the hollow interior?
- 216 cm³ (Correct answer)
- 512 cm³
- 343 cm³
- 64 cm³
Correct answer: 216 cm³
Inner edge = 8 − 2(1) = 6 cm; inner volume = 6³ = 216 cm³.
Bluebook SAT Test Area and Volume 10
An equilateral triangle has side length 8.
What is its area? (Leave answer in simplified radical form.)