Volume and Surface Area Foundations
A free Pre-Algebra lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Volume measures how much space a solid figure fills. For a rectangular prism, multiply length times width times height. Surface area measures the total area of the outside faces. In Geometry Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Find volume of rectangular prisms
- Find missing dimensions from volume
- Use surface area as the sum of face areas
Worked example
Problem. Find the volume of a rectangular prism that is 6 by 4 by 3.
- Use volume = length x width x height.
- 6 x 4 x 3 = 72.
- The volume is 72 cubic units.
- Connect the calculation back to Volume and Surface Area Foundations so the method, not just the arithmetic, is clear.
Answer: 72
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response). Counts include repeated prompts and variants.
Practice problems
1. Find the volume of a box that is 5 by 4 by 2.
Show solution
- Multiply length x width x height.
- 5 x 4 x 2 = 40.
Answer: 40
2. A cube has side length 3. What is its volume?
Show solution
- Volume = side x side x side.
- 3 x 3 x 3 = 27.
Answer: 27
3. A rectangular prism has length 8, width 2, and height 6. What is its volume?
Show solution
- Multiply 8 x 2 x 6.
- The volume is 96.
Answer: 96
4. A prism has volume 60, length 5, and width 4. What is its height?
Show solution
- Use 5 x 4 x height = 60.
- 20 x height = 60, so height = 3.
Answer: 3
5. Find the area of one face that is 7 by 3.
Show solution
- Face area is length x width.
- 7 x 3 = 21.
Answer: 21
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