Curved Surface Area of a Cone
If a perpendicular cut is made from a point on the circumference of the base to the vertex and the cone is opened up, a sector of a circle with radius is produced. Since the circumference of the base of the cone is , therefore the arc length of the sector of the circle is .
Where
slant height of the cone
radius of the base of the cone
Total Surface Area
The total surface area area of curved surface area of base
Rule:

The curved surface area of a right circular cone equals the perimeter of the base times onehalf slant height.

The total surface area equals the curved surface area of the base.
Example:
The slant height of a conical tomb is m. If its diameter is m, find the cost of cleaning it at $2 per cubic meter and also the cost of whitewashing the curved surface at cents per square meter.
Solution:
Now, slant height, m
Perpendicular height m (as )
Volume of the conical tomb
cubic meters
Cost of construction
Curved surface square meters
Cost of white washing dollars