Difference Between Total Surface Area (TSA) and Curved Surface Area (CSA)
Curved Surface Area (CSA)
Definition:
Curved Surface Area means the area of only the curved part of a solid.
👉 It does NOT include the top and bottom flat surfaces.
📦 Practical Examples:
🧃 Cold drink can – Only the side label area is CSA.
🎂 Cake (round shape) – Only the outer curved cream layer is CSA.🛢️ Gas cylinder – The painted round side part is CSA.
Total Surface Area (TSA)
Definition:
Total Surface Area means the area of all surfaces together.
👉 It includes:
Curved surface
Top surfaceBottom surface
📦 Practical Examples:
🎁 Wrapping a full gift box (covering everything)
🧃 Covering entire cold drink can including top & bottom
🎂 Covering whole cake including upper and lower surfaces
Example Using Cylinder
Consider a cylinder of radius r and height h.
🔸 Curved Surface Area (CSA)
CSA = 2 πrh
🔸 Total Surface Area (TSA)
TSA = 2πrh + 2πr^2
👉 TSA = CSA + Area of top + Area of bottom
Easy Comparison Table
| Feature | Curved Surface Area (CSA) | Total Surface Area (TSA) |
|---|---|---|
| Includes curved part | ✅ Yes | ✅ Yes |
| Includes top surface | ❌ No | ✅ Yes |
| Includes bottom surface | ❌ No | ✅ Yes |
| Used in | Labeling, side painting | Wrapping completely |
Example Calculation
Cylinder with:
Radius = 7 cm
Height = 10 cm
(Use π = 22/7)
CSA
= 2 × 22/7 × 7 × 10
= 440 cm²
TSA
= 440 + 2 × 22/7 × 49
= 440 + 308
= 748 cm²
🔥 Quick Exam Trick
If question says:
"Area to paint the side only" → CSA
"Area to cover completely" → TSA"Label area of bottle" → CSA
"Total covering area" → TSA
🎯 One-Line Summary
👉 CSA = Only curved part
👉 TSA = Curved part + top + bottom