The rules that solve most questions
- Rectangular prism: V = lwh. Cylinder: V = πr²h. Cone and pyramid: one third of the matching prism or cylinder.
- If lengths scale by k, areas scale by k² and volumes by k³.
- Use the radius, not the diameter, in circle formulas.
Traps the wrong answers are built on
- Multiplying the area by k instead of k² after scaling.
- Using the diameter as the radius.
Worked example
A triangle has an area of 9 square centimeters. Each side of the triangle is multiplied by 4 to make a larger, similar triangle. What is the area of the larger triangle, in square centimeters?
- A. 576
- B. 36
- C. 144
- D. 13
Answer: C. When lengths are scaled by 4, areas are scaled by 4² = 16. 9 × 16 = 144 square centimeters. Multiplying the area by 4 (giving 36) is the trap.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Harder
A triangle has an area of 9 square centimeters. Each side of the triangle is multiplied by 4 to make a larger, similar triangle. What is the area of the larger triangle, in square centimeters?
Show answer and explanation
Answer: C
When lengths are scaled by 4, areas are scaled by 4² = 16.
9 × 16 = 144 square centimeters.
Multiplying the area by 4 (giving 36) is the trap.
- Question 2Harder
A triangle has an area of 9 square centimeters. Each side of the triangle is multiplied by 4 to make a larger, similar triangle. What is the area of the larger triangle, in square centimeters?
Show answer and explanation
Answer: C
When lengths are scaled by 4, areas are scaled by 4² = 16.
9 × 16 = 144 square centimeters.
Multiplying the area by 4 (giving 36) is the trap.
- Question 3Harder
A triangle has an area of 12 square centimeters. Each side of the triangle is multiplied by 2 to make a larger, similar triangle. What is the area of the larger triangle, in square centimeters?
Show answer and explanation
Answer: A
When lengths are scaled by 2, areas are scaled by 2² = 4.
12 × 4 = 48 square centimeters.
Multiplying the area by 2 (giving 24) is the trap.
- Question 4Easier
A rectangular box is 9 inches long, 12 inches wide and 12 inches tall. What is its volume, in cubic inches?
Show answer and explanation
Answer: A
Volume = length × width × height = 9 × 12 × 12 = 1296 cubic inches.
- Question 5Easier
A rectangular box is 11 inches long, 5 inches wide and 4 inches tall. What is its volume, in cubic inches?
Show answer and explanation
Answer: C
Volume = length × width × height = 11 × 5 × 4 = 220 cubic inches.
- Question 6Easier
A rectangular box is 7 inches long, 11 inches wide and 11 inches tall. What is its volume, in cubic inches?
Show answer and explanation
Answer: D
Volume = length × width × height = 7 × 11 × 11 = 847 cubic inches.
- Question 7Medium
A right circular cylinder has a radius of 4 and a height of 11. What is its volume?
Show answer and explanation
Answer: B
Volume of a cylinder = πr²h.
π(4)²(11) = π × 16 × 11 = 176π.
Using the diameter (8) instead of the radius gives 704π, a common slip.
- Question 8Medium
A right circular cylinder has a radius of 4 and a height of 4. What is its volume?
Show answer and explanation
Answer: A
Volume of a cylinder = πr²h.
π(4)²(4) = π × 16 × 4 = 64π.
Using the diameter (8) instead of the radius gives 256π, a common slip.
- Question 9Harder
A triangle has an area of 17 square centimeters. Each side of the triangle is multiplied by 4 to make a larger, similar triangle. What is the area of the larger triangle, in square centimeters?
Show answer and explanation
Answer: D
When lengths are scaled by 4, areas are scaled by 4² = 16.
17 × 16 = 272 square centimeters.
Multiplying the area by 4 (giving 68) is the trap.
- Question 10Medium
A right circular cylinder has a radius of 6 and a height of 8. What is its volume?
Show answer and explanation
Answer: B
Volume of a cylinder = πr²h.
π(6)²(8) = π × 36 × 8 = 288π.
Using the diameter (12) instead of the radius gives 1152π, a common slip.
More Geometry and Trigonometry practice
Questions people ask
Is this area and volume practice like the real SAT?
The questions follow the format of the digital SAT's Geometry and Trigonometry domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Geometry and Trigonometry is one of the four content domains of the SAT Math section, alongside Algebra, Advanced Math, Problem-Solving and Data Analysis.