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SAT Math

Area and Volume

Area and Volume is a skill in the Geometry and Trigonometry domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

12 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

A rectangular storage box has dimensions 8 inches by 5 inches by 6 inches, giving it a volume of 240 cubic inches. If each dimension of the box is doubled to create a larger, similarly shaped box, what is the volume of the larger box, in cubic inches?
  1. A. 1,920 ✓
  2. B. 480
  3. C. 1,440
  4. D. 960

Correct answer: A. When every linear dimension of a solid is scaled by a factor of 2, the volume scales by 2³ = 8, so the new volume is 240 × 8 = 1,920 cubic inches.

A cylindrical water tank has a radius of 6 feet and a height of 10 feet. What is the volume of the tank, in cubic feet, in terms of π?
  1. A. 60π
  2. B. 360π ✓
  3. C. 1,440π
  4. D. 192π

Correct answer: B. The volume of a cylinder is V = πr²h = π(6²)(10) = π(36)(10) = 360π cubic feet.

Triangle ABC is similar to triangle DEF, where side DE corresponds to side AB and DE = 3 × AB. If the perimeter of triangle ABC is 18, what is the perimeter of triangle DEF?
  1. A. 6
  2. B. 162
  3. C. 54 ✓
  4. D. 21

Correct answer: C. Perimeter is a linear measurement, so it scales by the same factor as the corresponding side lengths; the perimeter of DEF is 18 × 3 = 54.

Two similar cylinders have radii in the ratio 2:5. If the volume of the smaller cylinder is 40 cubic centimeters, what is the volume of the larger cylinder, in cubic centimeters?
  1. A. 625 ✓
  2. B. 250
  3. C. 100
  4. D. 1000

Correct answer: A. Correct — for similar solids, volume scales with the cube of the linear scale factor; the scale factor from smaller to larger is 5/2, so the volume ratio is (5/2)³ = 125/8, giving 40 × 125/8 = 625.

A solid is formed by a cylinder with radius 3 and height 10, topped with a hemisphere of the same radius. What is the volume of the solid, in terms of π?
  1. A. 90π
  2. B. 108π ✓
  3. C. 126π
  4. D. 117π

Correct answer: B. Correct — the cylinder's volume is π(3²)(10) = 90π, and the hemisphere's volume is (2/3)π(3³) = 18π; the total is 90π + 18π = 108π.