The curved surface area (CSA) of a cone can be calculated using the formula:
Curved Surface Area (CSA) = πrl
Where:
- π is a mathematical constant approximately equal to 3.14159.
- r is the radius of the base of the cone.
- l is the slant height of the cone.
To understand why we use this formula, consider the shape of the cone. The curved surface area refers to the area of the cone’s lateral surface, excluding the base. When you “unroll” the cone, it turns into a sector of a circle. The radius of this sector corresponds to the slant height (l) of the cone, and the arc length of the base of the cone corresponds to the circumference of the base, which is 2πr.
Therefore, when calculating the CSA, we are essentially calculating the area of this curved surface, which is like finding the area of a triangle (with height l and base equal to the circumference of the base of the cone) or using the circular sector approach. Thus, the formula CSA = πrl results directly from this geometric relationship.
So, if you know the slant height and the radius of the cone, you can easily calculate its curved surface area by plugging those values into the formula.