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Area and volume — SAT practice questions

Area and volume on the SAT Math test covers perimeter and side length of squares, volume of a cylinder, and volume of similar solids. A student has to convert a perimeter difference into a side-length difference, write volume in terms of height, and scale volume by the cube of a linear factor. Items are short word problems with numeric or algebraic choices. Common traps are treating a 24-inch perimeter gap as the same side-length gap, mixing a radius of 7 centimeters with diameter, and multiplying 27 cubic units by 2 instead of by the cube of 2 when every linear dimension of statue B is twice that of statue A.

  • Section: Math 44 questions on the paper
  • 110 practice questions in the app

Sample questions

Question 1

Square MM has a perimeter that is 24 inches greater than the perimeter of square NN. By how many inches is the side length of square MM greater than the side length of square NN?

  1. A6
  2. B8
  3. C12
  4. D24
Show answer

Answer: A — 6

Perimeter difference divided by 4 gives the side-length difference: 24÷4=624\div4=6.

Question 2

A cylindrical vase has a radius of 7 centimeters and a height of hh centimeters. Which expression represents the volume, in cubic centimeters, of the vase in terms of hh?

  1. A14hπ14h\pi
  2. B7hπ7h\pi
  3. C98hπ98h\pi
  4. D49hπ49h\pi
Show answer

Answer: D — 49hπ49h\pi

Volume is πr2h=π(7)2h=49hπ\pi r^2h=\pi(7)^2h=49h\pi.

Question 3

Statue AA and statue BB are similar solids. Each linear dimension of statue BB is 2 times the corresponding dimension of statue AA. The volume of statue AA is 27 cubic units. What is the volume, in cubic units, of statue BB?

  1. A54
  2. B108
  3. C216
  4. D432
Show answer

Answer: C — 216

Scaling linear dimensions by 2 scales volume by 23=82^3=8, so the volume of BB is 27×8=21627\times8=216.

Practice 110 Area and volume questions in the app

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