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 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
