**height of a cone given lateral surface area is 67 and diameter is 8**

lateral surface area = 67

diameter = 8

radius = 8 / 2

radius = 4

slant height = 67 / ( PI * 4 )

slant height = 5.3295

slant height = 5.3295

height = sqrt( 5.3295 * 5.3295 - 4 * 4 )

height = 3.5219

where,

d = diameter

A = area

C = circumference

r = radius

V = volume

LSA = lateral surface area

TSA = total surface area

s = slant height

h = height