Lesson 11: Geometry: Volume & Surface Area
Volume measures how much 3D space a shape occupies (cubic units). Surface area measures the total area of all exterior faces. Both are essential in packaging, construction, and science.
Key Concepts
Rectangular Prism (Box)
Volume = length × width × height = lwh. Surface Area = 2(lw + lh + wh). Think: volume fills the inside, surface area wraps the outside.
Cylinder
Volume = πr²h. Surface area = 2πr² + 2πrh (two circles + the rolled rectangle). Common in cans, pipes, tanks.
Pyramid & Cone
Pyramid volume = ⅓ × base area × height. Cone volume = ⅓πr²h. The ⅓ factor comes from the fact that 3 pyramids fill 1 prism of the same base and height.
Sphere
Volume = (4/3)πr³. Surface area = 4πr². The surface area of a sphere equals exactly 4 circles of the same radius — a beautiful geometric fact.
🔬 Interactive Lab: Geometry: Volume & Surface Area Lab
✅ Check Your Understanding
1. Volume of a box with l=5, w=4, h=3 is:
2. The formula for the volume of a cylinder is:
3. What does surface area measure?