Mensuration >> Right Circular Cone

Height of a cone given lateral surface area and diameter - Right Circular Cone - Mensuration problem solver

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

height of a cone given lateral surface area and diameter

lateral surface area = 67
diameter = 8
r =  d / 2
radius = 8 / 2
radius = 4
So the radius is 4
s =  LSA / ( PI * r )
slant height = 67 / ( PI * 4 )
slant height = 5.3295
So the slant height is 5.3295
slant height = 5.3295
h =  sqrt( s * s - r * r )
height = sqrt( 5.3295 * 5.3295 - 4 * 4 )
height = 3.5219
So the height is 3.5219

Right circular cone Formulas :

A =  PI * r * r

C =  2 * PI * r

d =  r * 2

r =  d / 2

V =  (1/3) * PI * r * r * h

LSA =  PI * r * sqrt( r * r + h * h )

TSA =  ( PI * r * r ) + ( PI * r * sqrt( r * r + h * h ))

s =  sqrt( r * r + h * h )

h =  sqrt( s * s - r * r )


where,

d = diameter
A = area
C = circumference
r = radius
V = volume
LSA = lateral surface area
TSA = total surface area
s = slant height
h = height

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