Math 1 Quiz: Volume Calculations
10 questions · exam conditions
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Volume CalculationsQuestion 1 of 10

A hexagonal prism and a cylinder have equal volumes. If the cylinder has radius 6 cm and height 10 cm, and the hexagonal prism has the same height, what is the area of the hexagonal base?

72π square cm
360π square cm
18π square cm
36π square cm
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Math 1 Quiz

Math 1 Quiz: Volume Calculations

Practice Volume Calculations in Math 1 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Volume Calculations, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A hexagonal prism and a cylinder have equal volumes. If the cylinder has radius 6 cm and height 10 cm, and the hexagonal prism has the same height, what is the area of the hexagonal base?

  1. 72π square cm
  2. 360π square cm
  3. 18π square cm
  4. 36π square cm (correct answer)
Explanation: When you encounter problems involving equal volumes of different shapes, your goal is to set up an equation using the volume formulas and solve for the unknown dimension. Start by finding the cylinder's volume. A cylinder's volume is V=πr2hV = \pi r^2 h, so with radius 6 cm and height 10 cm: V=π(6)2(10)=360πV = \pi (6)^2 (10) = 360\pi cubic cm. Since the hexagonal prism has equal volume and the same height (10 cm), you can use the prism volume formula: V=base area×heightV = \text{base area} \times \text{height}. Setting up the equation: 360π=base area×10360\pi = \text{base area} \times 10 Solving for the hexagonal base area: base area=360π10=36π\text{base area} = \frac{360\pi}{10} = 36\pi square cm. Let's examine why the other answers are incorrect. Choice A (72π) represents double the correct answer—this might result from incorrectly doubling the base area calculation. Choice B (360π) is actually the total volume of both shapes, not the base area; this is a common trap where students confuse volume with area. Choice C (18π) is exactly half the correct answer, likely from an error in the division step (perhaps dividing by 20 instead of 10). The key strategy here is to always check your units: volume problems give you cubic units, but when solving for area, your final answer should be in square units. Also, remember that "equal volumes" problems are essentially proportion problems—set the volume formulas equal to each other and solve for the unknown.

Question 2

A triangular prism has a right triangular base with legs of 5 cm and 12 cm. If the prism's length is 15 cm, what is its volume?

  1. 900 cubic cm
  2. 450 cubic cm (correct answer)
  3. 1350 cubic cm
  4. 675 cubic cm
Explanation: Area of triangular base = (1/2) × 5 × 12 = 30 cm². Volume = base area × length = 30 × 15 = 450 cm³. Choice A uses the full rectangle area (5 × 12 × 15). Choice C incorrectly uses the hypotenuse in calculation. Choice D uses an incorrect base area calculation.

Question 3

A cylindrical grain silo has an internal diameter of 14 feet and a height of 25 feet. If grain fills the silo to a depth where the volume of grain equals the volume of a cone with the same base and height, what is the depth of the grain?

  1. 8.33 feet (correct answer)
  2. 12.5 feet
  3. 16.67 feet
  4. 6.25 feet
Explanation: Cone volume = (1/3)πr²h = (1/3)π(7²)(25) = (1225π)/3. For cylindrical volume to equal this: π(7²)(d) = (1225π)/3, where d is depth. Solving: 49πd = (1225π)/3, so d = 1225/(3×49) = 1225/147 = 25/3 ≈ 8.33 feet. Choice B is half the total height. Choice C is 2/3 of total height. Choice D is 1/4 of total height.

Question 4

Three identical square pyramids are arranged so their bases form a larger square. If each small pyramid has base edge 4 cm and height 9 cm, and they don't overlap, what is the total volume of the three pyramids?

  1. 48 cubic cm
  2. 432 cubic cm
  3. 144 cubic cm (correct answer)
  4. 216 cubic cm
Explanation: When you encounter pyramid volume problems, remember that the volume formula for any pyramid is V=13×base area×heightV = \frac{1}{3} \times \text{base area} \times \text{height}. This question tests whether you can apply this formula correctly and avoid calculation traps. For each square pyramid, you need the base area first. Since each pyramid has a square base with edge length 4 cm, the base area is 42=164^2 = 16 square cm. With height 9 cm, each pyramid's volume is V=13×16×9=1443=48V = \frac{1}{3} \times 16 \times 9 = \frac{144}{3} = 48 cubic cm. Since you have three identical pyramids, the total volume is 3×48=1443 \times 48 = 144 cubic cm, which is answer C. Looking at the wrong answers: A) 48 cubic cm gives you the volume of just one pyramid - you forgot to multiply by 3. This is a common oversight when problems mention multiple identical objects. B) 432 cubic cm likely comes from calculating 16×9×3=43216 \times 9 \times 3 = 432, forgetting the crucial 13\frac{1}{3} factor in the pyramid volume formula. D) 216 cubic cm might result from incorrectly calculating the base area as 4×4×3=484 \times 4 \times 3 = 48 instead of 16, then getting 13×48×9×3\frac{1}{3} \times 48 \times 9 \times 3. The detail about the pyramids forming a larger square is irrelevant information - focus only on what you need for the volume calculation. Always double-check that you're using the complete pyramid volume formula and accounting for all objects mentioned.

Question 5

A right triangular prism has a base with legs 9 cm and 12 cm. If the volume is 810 cubic cm, and the prism is then cut parallel to its triangular base to create two pieces where the smaller piece has 1/3 the volume of the original, what is the length of the smaller piece?

  1. 10 cm
  2. 15 cm
  3. 7.5 cm
  4. 5 cm (correct answer)
Explanation: When you encounter volume problems involving prisms cut parallel to their base, you're working with proportional scaling. The key insight is that volume scales with the cube of linear dimensions. First, let's find the original prism's height. The triangular base has legs 9 cm and 12 cm, so its area is 12×9×12=54\frac{1}{2} \times 9 \times 12 = 54 square cm. Since volume equals base area times height: 810=54×h810 = 54 \times h, so h=15h = 15 cm. The smaller piece has 13\frac{1}{3} the original volume, meaning 270270 cubic cm. Since it's cut parallel to the base, it's also a right triangular prism with the same base area (54 square cm). Therefore, its height is 27054=5\frac{270}{54} = 5 cm. Looking at the wrong answers: A) 10 cm might tempt you if you mistakenly think the smaller piece should be 23\frac{2}{3} of the original height. B) 15 cm is the original prism's total height, not the smaller piece. C) 7.5 cm could result from incorrectly assuming the cut divides the prism in half rather than creating a 13\frac{1}{3} volume ratio. The correct answer is D) 5 cm. Remember: when a prism is cut parallel to its base, both pieces maintain the same cross-sectional area as the original. This means volume is directly proportional to height, making these problems much simpler than they initially appear. Always start by finding the original dimensions, then use the given volume ratio to determine the piece's height.

Question 6

A cylindrical water tank has a radius of 4 meters and height of 12 meters. If the water level is currently at 75% capacity, how many cubic meters of water can still be added?

  1. 48π cubic meters (correct answer)
  2. 144π cubic meters
  3. 36π cubic meters
  4. 192π cubic meters
Explanation: Total volume = πr²h = π(4²)(12) = 192π m³. Current water = 75% × 192π = 144π m³. Remaining capacity = 192π - 144π = 48π m³. Choice B is the current water volume. Choice C represents 75% of 48π (incorrect calculation). Choice D is the total tank volume.

Question 7

A pentagonal prism has a base area of 45 square cm and a height that is twice the side length of the pentagon. If the side length is 6 cm, what is the volume of the prism?

  1. 540 cubic cm (correct answer)
  2. 1080 cubic cm
  3. 270 cubic cm
  4. 810 cubic cm
Explanation: Height = 2 × side length = 2 × 6 = 12 cm. Volume = base area × height = 45 × 12 = 540 cm³. Choice B doubles the correct answer. Choice C uses height = side length instead of twice. Choice D uses an incorrect height calculation.

Question 8

A rectangular prism has dimensions 6 cm × 8 cm × 10 cm. If the length is increased by 25% and the width is decreased by 12.5%, what is the new volume?

  1. 480 cubic cm
  2. 525 cubic cm (correct answer)
  3. 420 cubic cm
  4. 600 cubic cm
Explanation: Original volume = 6 × 8 × 10 = 480 cm³. New length = 6 × 1.25 = 7.5 cm. New width = 8 × 0.875 = 7 cm. Height remains 10 cm. New volume = 7.5 × 7 × 10 = 525 cm³. Choice A is the original volume. Choice C results from incorrectly decreasing both dimensions. Choice D results from only applying the length increase.

Question 9

A cone and a cylinder have the same radius and height. If the cylinder's volume is 240π cubic units, what is the volume of the cone?

  1. 720π cubic units
  2. 120π cubic units
  3. 80π cubic units (correct answer)
  4. 160π cubic units
Explanation: Volume of cylinder = πr²h = 240π. Volume of cone = (1/3)πr²h = (1/3) × 240π = 80π cubic units. Choice A incorrectly multiplies by 3. Choice B uses 1/2 instead of 1/3. Choice D uses 2/3 instead of 1/3.

Question 10

A rectangular swimming pool is 20 feet long, 12 feet wide, and has an average depth of 5 feet. If the pool is currently 80% full, how many more cubic feet of water are needed to fill it completely?

  1. 1200 cubic feet
  2. 240 cubic feet (correct answer)
  3. 960 cubic feet
  4. 300 cubic feet
Explanation: Total volume = 20 × 12 × 5 = 1200 ft³. Current water = 80% × 1200 = 960 ft³. Additional water needed = 1200 - 960 = 240 ft³. Choice A is the total volume. Choice C is the current water volume. Choice D represents 25% of the total volume.