Mrs.D Math · 8th Grade

WRAP
STAR

Surface Area of Cylinders · Geometry
📏 Surface Area
🥫 Cylinders
S = 2πrh + 2πr²
🪙 Total = Wrap + 2 Lids
🎈 Lateral = Just the Wrap
🧮 Use 3.14 for π
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📚 Surface Area of Cylinders

The Formula

A cylinder’s surface is made of a rectangle that wraps around the side plus two circle lids (top and bottom).

🎈
Lateral Surface Area — just the wrap (like a soup can label).
S = 2πrh
🪙
Total Surface Area — the wrap PLUS both circles.
S = 2πrh + 2πr²
🧮
Always use 3.14 for π in this game. Your calculator is waiting in the bottom-left corner. Type the WHOLE problem in — it has π, x², √, and ( ) buttons and follows order of operations when you press =.

Worked Example (from the lesson video!)

Radius = 5 in, Height = 9 in. Find the total surface area.

1
Write the formula.
S = 2πr² + 2πrh
2
Plug in the numbers.
S = 2(3.14)(5)² + 2(3.14)(5)(9)
3
Square first, then multiply.
S = 2(3.14)(25) + 2(3.14)(45) = 157 + 282.6
✓
Add them up! S = 439.6 in²

How to Play

📐
Surface Area — straight-up cylinder problems with a picture. Watch the badge: it tells you if the question wants TOTAL or LATERAL!
🌎
Real World — soup cans, silos, tanks, and drums. A label wrapping the side is lateral; covering the whole thing is total.
🎗
Mixed — both kinds together! On Medium and Hard, some questions flip it around and ask you to find the height.
✏️
Some questions are multiple choice, others make you type the answer. Round exactly as computed with 3.14 — no extra rounding needed!
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TOTAL SURFACE AREA
📺 Mrs.D Math Lesson
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