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ACT Area, perimeter & volume practice questions

Area, perimeter & volume sits in the Geometry reporting category on the ACT Math section. Prep36 has 11 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

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What Area, perimeter & volume covers on the ACT

Within this skill the Prep36 bank covers finding area from perimeter and one side, volume of a cylinder, perimeter of a rectangle, volume of composite solids, circle area from circumference and composite solid volume.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 11 questions tagged here is 4 easier, 2 medium and 5 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 area, perimeter & volume questions, with the reasoning

Question 1 easy

A rectangle has a perimeter of 46 centimeters and a length of 15 centimeters. What is the area, in square centimeters, of the rectangle?

  1. A. 23
  2. B. 31
  3. C. 120 correct
  4. D. 345
Why: The two lengths account for 30 cm, so the two widths total 46 - 30 = 16 cm and each width is 8 cm, making the area 15 × 8 = 120 square centimeters. The choice 23 is half the perimeter, and 31 is the width found by subtracting only one length instead of two. The choice 345 uses that same wrong width of 23 as if it were a side. Tip: in perimeter problems, subtract both copies of the known side before splitting what remains.
Question 2 medium

A right circular cone has a radius of 6 centimeters and a volume of 96π cubic centimeters. What is the height of the cone, in centimeters?

  1. A. 8/3
  2. B. 8 correct
  3. C. 32
  4. D. 96
Why: Cone volume is (1/3)πr²h, so (1/3)π(36)h = 96π gives 12πh = 96π and h = 8. Choice 8/3 drops the 1/3 and uses the cylinder formula πr²h, 32 is 96 ÷ 3 with the radius ignored, and 96 just repeats the volume number without solving anything. Tip: When you are given a volume and asked for a missing dimension, write the full formula, plug in every known value, and solve algebraically rather than dividing numbers that happen to be in the problem.
Question 3 hard

A grain silo is shaped like a right circular cylinder with a hemisphere on top. The cylinder has a radius of 3 feet and a height of 8 feet, and the hemisphere has the same radius of 3 feet. What is the total volume of the silo, in cubic feet?

  1. A. 72π
  2. B. 81π
  3. C. 108π
  4. D. 90π correct
Why: Break the solid into its two pieces and add. The cylinder holds πr²h = π(3²)(8) = 72π, and the hemisphere holds half of (4/3)π(3³) = half of 36π = 18π, so the total is 72π + 18π = 90π cubic feet. The choice 72π forgets the dome entirely, 108π adds a full sphere instead of half of one, and 81π uses an incorrect hemisphere value. Tip: With composite solids, compute each piece on its own line and label it before adding. The single most common slip is forgetting to halve the sphere, so write "half" next to that term as you go.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 11

The other 8 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

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Frequently asked questions

How many ACT area, perimeter & volume questions does Prep36 have?
11, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
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