Formula for the Curved Surface Area of a Cylinder (CSA)

A cylinder is a 3D shape with two parallel circular bases connected by a curved surface (like a tin can or a water pipe). In geometry and mensuration, calculating the area of this curved wall is a very common task.

Question (Click to Flip)

What if the diameter is given instead of the radius?

Answer

Since diameter is exactly twice the radius ($d = 2r$), you can simply divide the diameter by 2 to get the radius before using the formula. Alternatively, you can use the formula $CSA = \pi d h$.

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Key Facts

If you unfold the curved surface of a cylinder, it actually forms a perfect rectangle. The length of this rectangle is the circumference of the circle ($2\pi r$) and the width is the height ($h$). Hence, Area = $2\pi r \times h$.

To find the Total Surface Area (TSA), you must add the area of the two circular bases to the CSA. Formula: $TSA = 2\pi rh + 2\pi r^2 = 2\pi r(h+r)$.

1. What is Curved Surface Area (CSA)?

The Curved Surface Area (also called Lateral Surface Area) refers only to the area of the curved, round wall of the cylinder. It does not include the flat circular top and the flat circular bottom.

2. The Formula

The formula to calculate the CSA of a cylinder is: $CSA = 2\pi rh$

Where:

$\pi$ (Pi) $\approx \frac{22}{7}$ or $3.14$
$r$ = Radius of the circular base
$h$ = Height of the cylinder

3. Example Calculation

Question: Find the curved surface area of a pipe with a radius of $7 \text{ cm}$ and a height of $10 \text{ cm}$.

$r = 7$, $h = 10$, $\pi = 22/7$
$CSA = 2 \times \frac{22}{7} \times 7 \times 10$
The 7s cancel out: $CSA = 2 \times 22 \times 10$
$CSA = 440 \text{ cm}^2$

(Note: Area is always written in square units).

Questions and Answers

What if the diameter is given instead of the radius?+

Since diameter is exactly twice the radius ($d = 2r$), you can simply divide the diameter by 2 to get the radius before using the formula. Alternatively, you can use the formula $CSA = \pi d h$.

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