Geometry and Trigonometry · Math
Area and volume
Area, surface area, and volume, including how those measures change when a figure is scaled.
19 questions in the bank · 5 easier · 9 medium · 5 harder · this domain is ≈15% of the section
What to watch for
When every length scales by k, areas scale by k² and volumes by k³. Treating area or volume as if it scaled linearly is the central trap.
How the question is worded
These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.
- A rectangle has a length of 12 centimeters and a width of 11 centimeters. What is the area of the rectangle, in square centimeters?
- A rectangle has a length of 6 centimeters and a width of 7 centimeters. What is the area of the rectangle, in square centimeters?
- A triangle has a base of 12 centimeters and a height of 7 centimeters. What is the area of the triangle, in square centimeters?
- A triangle has a base of 18 centimeters and a height of 7 centimeters. What is the area of the triangle, in square centimeters?
Worked examples
easyA rectangle has a length of 12 centimeters and a width of 11 centimeters. What…
A rectangle has a length of 12 centimeters and a width of 11 centimeters. What is the area of the rectangle, in square centimeters?
Answer: 132
Explanation
Rectangle area is length · width: 12 · 11 = 132 square centimeters.
mediumA right circular cylinder has a radius of 4 inches and a height of 8 inches. W…
A right circular cylinder has a radius of 4 inches and a height of 8 inches. What is the volume of the cylinder, in cubic inches?
- A. 32π
- B. 64π
- C. 128π
- D. 512π
Answer: C. 128π
Explanation
Cylinder volume is (area of the circular base) · height = πr²h = π · 4² · 8 = 128π cubic inches. Squaring the radius before multiplying is where the wrong answers diverge.
hardA solid has volume 6 cubic units. Each side length of the solid is multiplied …
A solid has volume 6 cubic units. Each side length of the solid is multiplied by 5 to create a similar solid. What is the volume of the new solid, in cubic units?
- A. 30
- B. 131
- C. 150
- D. 750
Answer: D. 750
Explanation
When lengths scale by k, areas scale by k² and volumes by k³. Here k = 5, so the volume scales by 5³ = 125: 6 × 125 = 750. Multiplying by k alone treats volume as a length — the central trap.