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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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Lateral Area of a Cone Formula

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