Lateral Area of a Cone Formula

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The formula for finding the lateral area of a cone is
 
L.A. = pi * r * l
 
where pi is a constant having value 22/ 7,

r is the radius of the cone’s base,

l is the slant height of the cone.
 
The slant height l of the cone can be found by using the formula
 
l = ( r2 + h2 )1/2
 
Where h is the height of the cone.


Example 1: Find the lateral area of a cone having radius = 8 cm, slant height = 14 cm.

Solution : We are given,

radius r = 8 cm

slant height l = 14 cm

The formula for lateral area of a cone is L.A. = pi * r * l

 
Putting the values in the formula,

L.A. = 22/7 * 8 * 14 = 2464 / 7 = 352
 
Thus the lateral area of the given cone is 352 square centimeters.

 
Example 2: Find the lateral area of a cone with radius = 6 cm, height = 8 cm.

Solution:

Slant height  l = ( r2 + h2 )1/2      
        
                       
l = ( 62 + 82 )1/2       
       

 l = ( 36  + 642 )1/2

 l = ( 100 )1/2

l = 10         
    
Now we can find the lateral area using the formula,

L.A. = pi * r * l

L.A. = 22/7 * 6 * 10 = 1320 / 7
 
L.A. = 188.6
 
Hence the lateral area the cone is 188.6 square centimeters.


 

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