The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Volume vs. surface area
Volume measures the space inside a 3-D figure (cubic units). Surface area is the total area of all the faces (square units).
Area measures how much space a flat shape covers, in square units. Picture tiles on a floor. Each tile is one square unit.
Break complicated shapes into rectangles or triangles you already know how to measure, then add the pieces together.
Prisms
- 1Volume of any prism = area of the base × height.
- 2Surface area = the sum of the areas of every face (use a net to keep track).
Find the volume of a box 4 cm × 3 cm × 2 cm.
- 1Base area = 4 × 3 = 12 cm².
- 2Volume = base × height = 12 × 2 = 24 cm³.
Why this matters
Find how much space a solid fills and the total area of its faces.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- Volume vs. surface area
- Prisms
- Volume of any prism = area of the base × height.
- Surface area = the sum of the areas of every face (use a net to keep track).
Video walkthroughs
Surface Area of a Rectangular Prism
Practice finding total surface area with a net.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfFind the volume of a rectangular prism 6 cm × 4 cm × 3 cm.
Step-by-step solution
- 1V = lwh = 6 × 4 × 3 = 72 cm³.
Exercise 2
Try it yourselfA cube has edge length 5 m. What is its volume?
Step-by-step solution
- 1V = s³ = 5³ = 125 m³.
Exercise 3
Try it yourselfA triangular prism has base area 12 ft² and height 8 ft. Find the volume.
Step-by-step solution
- 1V = Bh = 12 × 8 = 96 ft³.
Exercise 4
Try it yourselfA box is 10 in × 5 in × 2 in. Find the surface area.
Step-by-step solution
- 1SA = 2(lw + lh + wh).
- 2lw = 50, lh = 20, wh = 10.
- 3SA = 2(50 + 20 + 10) = 2(80) = 160 in².
Exercise 5
Try it yourselfA cylinder has radius 3 cm and height 10 cm. Find the volume (π ≈ 3.14).
Step-by-step solution
- 1V = πr²h = 3.14 × 9 × 10 = 282.6 cm³.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Volume & Surface Area
Question 1 of 4
A rectangular prism is 5 × 2 × 3. What is its volume?