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 out, 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:
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 dollar 2 per cubic meter and also the cost of whitewashing the curved surface at cent per square meter.
Solution:
Now, slant height, m
Perpendicular height m (as )
Volume of the conical tomb
Cubic Meter
Cost of construction
Curved Surface Square Meter
Cost of white washing Dollar