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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 one-half 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 
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