To understand how much area a cylinder occupies from the outside, we use its surface area formula. Cylinders appear everywhere, in water tanks, pipes, cold drink cans, candles, drums, and even machine parts. Knowing how to calculate their surface area helps in tasks like painting, wrapping, covering, and designing cylindrical objects.
In maths and competitive exams, the surface area of a cylinder is one of the most frequently asked concepts because it connects geometry, measurement, and real-world applications.
Formula for the Surface Area of a Cylinder – Quick Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| TSA = 2πr(h + r) | r = radius, h = height, π = 3.1416 | Used to find total outer area of a cylinder |
What is the Surface Area of a Cylinder in Maths?
The surface area of a cylinder represents the complete area covered by all its faces, the curved surface plus the two circular bases. It is always measured in square units like cm², m², or mm².
A cylinder has:
- Two flat circular bases
- One curved surface that wraps around the height
So, the total surface area (TSA) is the sum of:
- Curved Surface Area (CSA) = 2πrh
- Area of two bases = 2πr²
Therefore, the formula becomes:
TSA = 2πr(h + r)
This formula is used frequently in practical tasks, from finding the paint required for tanks to calculating the metal needed for manufacturing cans. It’s also a common topic in CUET, SSC, Banking, JEE, and school-level exams.
Examples to Calculate Surface Area of a Cylinder
Example 1: r = 5 cm, h = 10 cm
Step 1: TSA = 2πr(h + r)
Step 2: = 2 × 3.14 × 5 × (10 + 5)
Step 3: = 6.28 × 5 × 15
Result: 471 cm²
So, the total surface area of the cylinder is 471 cm².
Example 2: r = 7 m, h = 14 m
Step 1: TSA = 2πr(h + r)
Step 2: = 2 × 3.14 × 7 × (14 + 7)
Step 3: = 6.28 × 7 × 21
Result: 923.76 m²
So, the total surface area of the cylinder is 923.76 m².
FAQs about Surface Area of a Cylinder Formula
Q1. What is the surface area of a cylinder?
It is the total area covering the curved surface and the two circular ends.
Q2. What are the units of surface area?
Always square units such as cm², m², or mm².
Q3. What is the curved surface area formula?
CSA of a cylinder = 2πrh.
Q4. What is the difference between TSA and CSA?
TSA includes both circular bases, while CSA only covers the curved outer surface.
Q5. Where is this formula used in real life?
Used for calculating paint, wrapping, metal covering, or labeling of cylindrical objects like pipes, cans, tanks, and bottles.
Q6. Why is π used in the formula?
Because the cylinder has circular bases, and π connects radius to circumference and area.