Area and volume — SAT practice questions

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Practice 110 Area and volume questions in the app

What this topic is

Area and volume questions draw on formulas the SAT supplies on a reference sheet, covering circles, rectangles, triangles, cylinders, cones, spheres and prisms.

Knowing which formula applies is rarely the hard part; reasoning about how measurements relate usually is. Scaling is a favorite idea: when every length of a figure is multiplied by k, its area is multiplied by k squared and its volume by k cubed.

A square's perimeter and side length change together, so the perimeter grows by four times any increase in the side. Answers are often left in terms of pi or of a variable such as height, and some are entered rather than chosen.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

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

6✓ Correct8✗ Not this one12✗ Not this one24✗ Not this one

Show answer

Answer: A — 6

Perimeter difference divided by 4 gives the side-length difference: $24 \div 4 = 6$ .

Question 2Easier

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

14 h π

✗ Not this one

7 h π

✗ Not this one

98 h π

✗ Not this one

49 h π

✓ Correct

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Answer: D — $49 h π$

Volume is $π r^{2} h = π (7)^{2} h = 49 h π$ .

Question 3Easier

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

54✗ Not this one108✗ Not this one216✓ Correct432✗ Not this one

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Answer: C — 216

Scaling linear dimensions by 2 scales volume by $2^{3} = 8$ , so the volume of $B$ is $27 \times 8 = 216$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 110 Area and volume questions in the app

Area and volume — SAT practice questions

What this topic is

Sample questions

More SAT topics

Math