CSA of Circle Formula

The formula for the curved surface area (CSA) of a circle is given by:

CSA = 2πrh

Where:
- r is the radius of the circle
- h is the height of the cylinder (which is equal to the circumference of the base)

Explanation

The curved surface area of a circle refers to the area of the circular part of a cylinder. In other words, it is the area of the side of the cylinder, excluding the top and bottom circles.

To calculate the CSA of a circle, you need to know the radius of the circle and the height of the cylinder. The radius is the distance from the center of the circle to any point on its circumference. The height of the cylinder is equal to the circumference of the circle, which is given by the formula:

Circumference = 2πr

Where:
- π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter (approximately 3.14159)
- r is the radius of the circle

Once you know the radius and circumference of the circle, you can use the formula for the CSA of a circle to find its area.

Example

Suppose you have a cylinder with a radius of 5 cm and a height of 10 cm. To find the CSA of the circle, you can use the following steps:

1. Find the circumference of the circle:
Circumference = 2πr = 2π(5) ≈ 31.4159 cm

2. Use the circumference as the height of the cylinder in the formula for CSA:
CSA = 2πrh = 2π(5)(31.4159) ≈ 314.159 cm²

Therefore, the CSA of the circle in this example is approximately 314.159 cm².

A circle has no curved surface area because it is not a three dimensional figure.