Calculate Prism Volume with Fractional Edge Lengths
Rename mixed lengths as fractions if needed, multiply all three dimensions, and simplify.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: A prism has sides 3/2,2/3,5/4 units.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
The prism volume formula applies to fractional lengths as well as whole lengths. Unit-fraction cubes can model the solid, or multiply the three lengths exactly as fractions. The result measures cubic units. A product below one is possible when a solid occupies less volume than a full unit cube.
Rename mixed lengths as fractions if needed, multiply all three dimensions, and simplify. Check using base area × height and estimate with nearby lengths. Keep cubic units on the result rather than confusing it with surface area.
Multiply all three dimensions, not only the base lengths. Volume has cubic units even when its value is a fraction. Compute and label the base area separately, then multiply by the fractional height.
- Compute and label the base area separately, then multiply by the fractional height.
- Work through the supplied example and label what each number or attribute represents.
- Rename mixed lengths as fractions if needed, multiply all three dimensions, and simplify.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
A prism has sides 3/2,2/3,5/4 units. Base area is (3/2)(2/3)=1 square unit, so volume is 5/4 cubic units. Direct three-factor multiplication agrees. The denominator parts describe subdivisions of lengths, and their product describes subdivisions of cube volume. Multiply all three dimensions, not only the base lengths. Volume has cubic units even when its value is a fraction. Compute and label the base area separately, then multiply by the fractional height.
Check your reasoning
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Helpful tips
- Multiply all three dimensions, not only the base lengths.
- Volume has cubic units even when its value is a fraction.
See the answer and explanation
5
Multiply all three exact fractional edge lengths. The result is 5.
Take it further
Edges 1/2,3/4,2 units give volume 3/4 cubic unit.
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