Build a Volume from a Base and Height
A rectangular prism’s volume equals its base area times its perpendicular height.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: A rectangular prism measures 2 cm by 3 cm by 4 cm. What is its volume? Candidate answers: (A) 24 cm³ (B) 52 cm³ (C) 6 cm³ (D) 9 cm³.
- Independent check inputs: A rectangular prism measures 3 cm by 4 cm by 5 cm. What is its volume? Candidate answers: (A) 12 cm³ (B) 60 cm³ (C) 62 cm³ (D) 94 cm³.
Learn the idea
Geometric measures answer different questions: circumference is boundary length, area covers a region, and volume counts space. A formula works only when its input dimensions and output units match the question being asked. A rectangular prism’s volume equals its base area times its perpendicular height. Each unit layer contains the same cross-section, connecting multiplication to a stack-of-layers model.
Here is the method on the supplied teaching case. One base has area 2×3=6 cm². Stack through a height of 4 cm: V=6×4=24 cm³.
Use three mutually perpendicular dimensions rather than adding edge lengths. A cubic unit describes a unit of space; the surface area of the box instead counts its exterior faces.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: A rectangular prism measures 2 cm by 3 cm by 4 cm. What is its volume? Candidate answers: (A) 24 cm³ (B) 52 cm³ (C) 6 cm³ (D) 9 cm³. Solution: One base has area 2×3=6 cm². Stack through a height of 4 cm: V=6×4=24 cm³. The final answer is 24 cm³. Use three mutually perpendicular dimensions rather than adding edge lengths. A cubic unit describes a unit of space; the surface area of the box instead counts its exterior faces.
Check your reasoning
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Helpful tips
- A rectangular prism’s volume equals its base area times its perpendicular height.
- Use three mutually perpendicular dimensions rather than adding edge lengths.
See the answer and explanation
60 cm³
One base has area 3×4=12 cm². Stack through a height of 5 cm: V=12×5=60 cm³.
Take it further
Changed-input task: A rectangular prism measures 9 cm by 10 cm by 11 cm. What is its volume? Candidate answers: (A) 30 cm³ (B) 598 cm³ (C) 90 cm³ (D) 990 cm³. Show the mathematical reason, not only the selected answer. Expected result: 990 cm³. One base has area 9×10=90 cm². Stack through a height of 11 cm: V=90×11=990 cm³.
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