Grade: Grade 5 Subject: Mathematics Unit: Volume Lesson: 5 of 6 SAT: Geometry + Trigonometry ACT: Math

Common Mistakes with Volume

Learn to identify and avoid common errors when calculating volume!

Why Mistakes Happen

Learning from Errors

Volume calculations require attention to all three dimensions. Most mistakes come from confusing area and volume or forgetting to use cubic units.

Mistake #1: Confusing Area and Volume

Wrong Way
Box: 4 x 3 = 12 cubic units

Only multiplying two dimensions (that's area, not volume!)

Right Way
Box: 4 x 3 x 2 = 24 cubic units

Multiply all THREE dimensions: length x width x height!

Remember: Area uses 2 dimensions (square units). Volume uses 3 dimensions (cubic units).

Mistake #2: Wrong Units

Wrong Way
V = 5 x 4 x 3 = 60 square cm

Using square units instead of cubic units!

Right Way
V = 5 x 4 x 3 = 60 cubic cm (or cm³)

Volume is always in CUBIC units!

Mistake #3: Not Decomposing Composite Figures

Wrong Way
L-shaped solid: 6 x 4 x 3 = 72 cu in

Treating an L-shape as one rectangle!

Right Way
Part A: 4 x 2 x 3 = 24 cu in
Part B: 2 x 4 x 3 = 24 cu in
Total: 24 + 24 = 48 cu in

Break into smaller rectangular prisms, find each volume, then add!

Mistake #4: Mixing Up Dimensions

Wrong Way
Given: l=5, w=3, h=4
V = 5 + 3 + 4 = 12

Adding dimensions instead of multiplying!

Right Way
Given: l=5, w=3, h=4
V = 5 x 3 x 4 = 60 cubic units

Volume = length x width x height (multiply!)

Pro Tip: Write out the formula V = l x w x h before plugging in numbers!

Practice: Spot the Mistake

Question 1

Is this correct? A box is 6 x 4 x 2 inches. Volume = 48 square inches.

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Incorrect! The math is right (6 x 4 x 2 = 48), but the units are wrong. It should be 48 CUBIC inches, not square inches.

Question 2

Is this correct? A cube with sides of 5 cm has a volume of 25 cubic cm.

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Incorrect! That's the area of one face. Volume = 5 x 5 x 5 = 125 cubic cm.

Question 3

Is this correct? V = 8 x 3 x 4 = 96 cubic meters.

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Correct! 8 x 3 = 24, and 24 x 4 = 96 cubic meters.

Question 4

Is this correct? An L-shaped figure made of two 3x2x2 boxes has volume = 12 cubic units.

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Incorrect! One box = 3 x 2 x 2 = 12. Two boxes = 12 + 12 = 24 cubic units.

Question 5

Is this correct? V = 7 + 5 + 3 = 15 cubic feet.

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Incorrect! You must MULTIPLY, not add. V = 7 x 5 x 3 = 105 cubic feet.

Question 6

Is this correct? A rectangular prism 10 x 4 x 5 has volume = 200 cubic units.

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Correct! 10 x 4 = 40, and 40 x 5 = 200 cubic units.

Question 7

Is this correct? To find volume of a box 4 x 6 x 3, first find area (24), then multiply by 3 to get 72.

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Correct! This method works! Base area (4 x 6 = 24) times height (3) = 72 cubic units.

Question 8

Is this correct? A cube with volume 27 cubic cm has sides of 9 cm each.

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Incorrect! If sides were 9, volume would be 9 x 9 x 9 = 729. The cube root of 27 is 3, so sides are 3 cm.

Question 9

Is this correct? Volume is measured in cubic units because we're measuring 3 dimensions.

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Correct! Cubic = three dimensions multiplied together (length x width x height).

Question 10

Is this correct? V = 2 x 2 x 2 = 6 cubic units.

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Incorrect! 2 x 2 = 4, and 4 x 2 = 8 cubic units, not 6.

Key Takeaways

Three Dimensions

Volume = l x w x h (multiply all three!)

Cubic Units

Always use cubic units for volume answers!

Decompose

Break complex shapes into smaller prisms!

Check Work

Ask: Did I multiply (not add) all three dimensions?