Mensuration >> Right Circular Cone

Height of a cone with lateral surface area - Right Circular Cone - Mensuration problem solver

The lateral surface area of a cone is 198.6 cm squared and the diameter of the cone is 10.2 cm determine the height of the cone

Height of a cone with lateral surface area

lateral surface area = 198.6
diameter = 10.2
r =  d / 2
radius = 10.2 / 2
radius = 5.1
So the radius is 5.1
s =  LSA / ( PI * r )
slant height = 198.6 / ( PI * 5.1 )
slant height = 12.3904
So the slant height is 12.3904
slant height = 12.3904
h =  sqrt( s * s - r * r )
height = sqrt( 12.3904 * 12.3904 - 5.1 * 5.1 )
height = 11.2921
So the height is 11.2921

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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