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.
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.
Answer: 180
Practice problems
1. Find the volume of a rectangular prism that is 6 by 5 by 4.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the volume of a rectangular prism that is 6 by 5 by 4.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 6 x 5 x 4 = 120.
- Check the result by substituting or estimating: the response should match 120 and make sense in the original problem.
Answer: 120
2. A cube has side length 5. What is its volume?
Show solution
- Warm-up: First identify exactly what the question is asking: A cube has side length 5. What is its volume?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 5 x 5 x 5 = 125.
- Check the result by substituting or estimating: the response should match 125 and make sense in the original problem.
Answer: 125
3. A prism has base area 18 and height 7. What is its volume?
Show solution
- Core Practice: First identify exactly what the question is asking: A prism has base area 18 and height 7. What is its volume?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 18 x 7 = 126.
- Check the result by substituting or estimating: the response should match 126 and make sense in the original problem.
Answer: 126
4. A rectangular prism has volume 180, length 9, and width 5. What is its height?
Show solution
- Core Practice: First identify exactly what the question is asking: A rectangular prism has volume 180, length 9, and width 5. What is its height?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 9 x 5 = 45.
- 180/45 = 4.
- Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.
Answer: 4
5. A rectangular prism has face areas 20, 30, and 24. What is its surface area?
Show solution
- Challenge: First identify exactly what the question is asking: A rectangular prism has face areas 20, 30, and 24. What is its surface area?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 2(20 + 30 + 24) = 148.
- Check the result by substituting or estimating: the response should match 148 and make sense in the original problem.
Answer: 148
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