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.
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.
Answer: 72
Practice problems
1. Find the volume of a box that is 5 by 4 by 2.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the volume of a box that is 5 by 4 by 2.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Multiply length x width x height.
- 5 x 4 x 2 = 40.
- Check the result by substituting or estimating: the response should match 40 and make sense in the original problem.
Answer: 40
2. A cube has side length 3. What is its volume?
Show solution
- Warm-up: First identify exactly what the question is asking: A cube has side length 3. What is its volume?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Volume = side x side x side.
- 3 x 3 x 3 = 27.
- Check the result by substituting or estimating: the response should match 27 and make sense in the original problem.
Answer: 27
3. A rectangular prism has length 8, width 2, and height 6. What is its volume?
Show solution
- Warm-up: First identify exactly what the question is asking: A rectangular prism has length 8, width 2, and height 6. What is its volume?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Multiply 8 x 2 x 6.
- The volume is 96.
- Check the result by substituting or estimating: the response should match 96 and make sense in the original problem.
Answer: 96
4. A prism has volume 60, length 5, and width 4. What is its height?
Show solution
- Core Practice: First identify exactly what the question is asking: A prism has volume 60, length 5, and width 4. What is its height?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Use 5 x 4 x height = 60.
- 20 x height = 60, so height = 3.
- Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.
Answer: 3
5. Find the area of one face that is 7 by 3.
Show solution
- Core Practice: First identify exactly what the question is asking: Find the area of one face that is 7 by 3.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Face area is length x width.
- 7 x 3 = 21.
- Check the result by substituting or estimating: the response should match 21 and make sense in the original problem.
Answer: 21
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