Bluebook SAT Test Area and Volume 3 — Questions and Answers
Question 1: What is the area of a circle with diameter 10? (Leave answer in terms of π)
- 10π
- 20π
- 25π (Correct answer)
- 100π
Correct answer: 25π
Radius = 5; Area = π(5²) = 25π.
Question 2: A rectangular prism has volume 180 cm³, length 9 cm, and width 4 cm. What is its height?
- 3 cm
- 5 cm (Correct answer)
- 7 cm
- 9 cm
Correct answer: 5 cm
h = V ÷ (l × w) = 180 ÷ 36 = 5 cm.
Question 3: The length of a rectangle is twice its width. If the area is 72 m², what is the width?
- 4 m
- 6 m (Correct answer)
- 8 m
- 9 m
Correct answer: 6 m
Let w = width, l = 2w; A = 2w² = 72 → w² = 36 → w = 6 m.
Question 4: A trapezoid has parallel sides of 8 cm and 12 cm, and a height of 5 cm. What is its area?
- 40 cm²
- 50 cm² (Correct answer)
- 80 cm²
- 100 cm²
Correct answer: 50 cm²
A = ½(b₁ + b₂)h = ½(8 + 12)(5) = ½ × 20 × 5 = 50 cm².
Question 5: A sphere's radius is tripled. By what factor does its volume increase?
- 3
- 9
- 27 (Correct answer)
- 81
Correct answer: 27
Volume ∝ r³; tripling r multiplies volume by 3³ = 27.
Question 6: A triangular prism has a triangular cross-section with base 6 m and height 4 m, and prism length 10 m. What is its volume?
- 60 m³
- 120 m³ (Correct answer)
- 240 m³
- 480 m³
Correct answer: 120 m³
V = (½ × 6 × 4) × 10 = 12 × 10 = 120 m³.
Question 7: A square has an area of 144 cm². What is the perimeter of the square?
- 12 cm
- 24 cm
- 36 cm
- 48 cm (Correct answer)
Correct answer: 48 cm
Side = √144 = 12 cm; Perimeter = 4 × 12 = 48 cm.
Bluebook SAT Test Area and Volume 3
What is the area of a circle with diameter 10? (Leave answer in terms of π)