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Surface Area of a Right Circular Cone


Surface Area of a Right Circular Cone

 

Area of the curved surface of a cone = prl = pr  sq. units where l=
Total surface area of a cone =
prl + pr2 = pr(l + r) sq. units
 

Example:

How many meters of cloth of 5m wide will be required to make a conical tent, the radius of the whole base is 7m and whose height is 24m ?
 

Solution:

Given , r=7m

         h = 24m

          l== = = 25

CSA of the cone = rl m2 = 7 25 = 550m2

Area of the canvas used = 550m2

Given , width of the canvas = 5m

Length of the canvas used = = m
 

 

Example:

From a cylinder of 12 m height and base radius 5 m, a conical cavity of the same height and same radius (base) is carved out. Find the whole surface area of the remaining solid.

Solution:

Surface area of the remaining solid= Area of a circle (base) + Area of the curved surface of the cylinder + Area of the curved surface of the cone.
=
pr2 + 2prh + prl

 
l = = = 13 m

\Total curved surface area = p(r2 + 2rh + rl)

              =
´ (52 + 2 ´ 5 ´ 12 + 5 ´ 13)

               =
´ 5(5 + 24 + 13)

              = 660 m
2
 

Surface area of the remaining solid = 660 m2
 





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