Surface Area and Volume
A free Geometry lesson from the “Measurement, Circles, and 3D Solids” unit, with a worked example and practice problems including step-by-step solutions.
Volume measures space inside a solid, while surface area measures the total area covering the outside. Prisms use volume = base area times height. In Measurement, Circles, and 3D Solids, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Find prism volume
- Find surface area
- Distinguish square and cubic units
Worked example
Problem. Find the volume of a rectangular prism that is 5 by 4 by 9.
- Volume = length x width x height.
- Multiply 5 x 4 x 9.
- The volume is 180 cubic units.
- Connect the result back to Surface Area and Volume so the geometric relationship is explicit.
Answer: 180
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Find the volume of a rectangular prism that is 6 by 5 by 4.
Show solution
- 6 x 5 x 4 = 120.
Answer: 120
2. A cube has side length 5. What is its volume?
Show solution
- 5 x 5 x 5 = 125.
Answer: 125
3. A prism has base area 18 and height 7. What is its volume?
Show solution
- 18 x 7 = 126.
Answer: 126
4. A rectangular prism has volume 180, length 9, and width 5. What is its height?
Show solution
- 9 x 5 = 45.
- 180/45 = 4.
Answer: 4
5. A rectangular prism has face areas 20, 30, and 24. What is its surface area?
Show solution
- 2(20 + 30 + 24) = 148.
Answer: 148
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