Surface Area of Prisms & Cylinders
Surface area = 2 bases + lateral area. For prisms and cylinders, the lateral area “unwraps” into a simple rectangle.
Introduction
Past Knowledge
Area formulas (11.1). Circumference (11.2.1). Nets of 3D shapes.
Today's Goal
Compute SA for prisms and cylinders using LA + 2B.
Future Success
Pyramid/cone SA (12.2.2–12.2.3), volume (12.3).
Key Concepts
Prism Surface Area
B = base area, P = base perimeter, h = height. Lateral area = Ph (perimeter × height).
Cylinder Surface Area
Two circular bases + lateral area (rectangle with width = circumference, height = h).
Worked Examples
Rectangular Prism
l = 6, w = 4, h = 3
SA = 108 sq units
Cylinder
r = 5, h = 10
SA = 150π ≈ 471.2
Common Pitfalls
Forgetting the Bases
SA = LA + 2B. Many students only compute lateral area and forget the two bases.
Cylinder LA Uses Circumference
Lateral area of a cylinder = 2πrh, NOT 2πr²h. The “width” of the rectangle is the circumference (2πr), not the area of the base.
Real-Life Applications
Gift Wrapping
To wrap a rectangular box, you need surface area of paper + overlap.
Label Design
A can label is the lateral area of a cylinder = 2πrh. This determines the label's width and height.
Practice Quiz
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