Mensuration >> Right Circular Cone

Height of a cylinder based on a cone - Right Circular Cone - Mensuration problem solver

A cone and cylinder have the same volume. The cone has a radius of 4cm and a slant height of 6cm. If the cylinder radius is 5cm, what is the height of the cylinder.

height of a cylinder based on a cone

radius = 4
slant height = 6
cylinder radius = 5
h =  sqrt( s * s - r * r )
height = sqrt( 6 * 6 - 4 * 4 )
height = 4.4721
So the height is 4.4721
V =  (1/3) * PI * r * r * h
volume = (1/3) * PI * 4 * 4 * 4.4721
volume = 74.9609
So the volume is 74.9609

volume = 74.9609
radius = 5
C =  2 * PI * r
circumference = 2 * PI * 5
circumference = 31.4286
So the circumference is 31.4286
h =  V / ( PI * r * r )
height = 74.9609 / ( PI * 5 * 5 )
height = 0.954
height = 0.954
CSA =  2 * PI * r * h
curved surface area = 2 * PI * 5 * 0.954
curved surface area = 29.9829
So the curved surface area is 29.9829
curved surface area = 29.9829

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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