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.