The volume of a right circular cone. whose radius of the base is one-third of its altitude. and the volume
of a hemisphere are equal. The ratio of the radii of the cone and the hemisphere is:
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❥i ) Dimensions of the right circular
cone :
radius = r units
altitude ( h ) = 2r units
Volume of
the cone = (π×radius² ×altitude)/3
➡ V1 = ( πr² × 2r )/3
➡ V1 = (2πr³ )/3 ---( 1 )
❥ii ) Let the radius of the Sphere = R units
Volume of the Sphere = (2/3 ) πR³ --( 2 )
according to the problem given ,
➡ ( 1 ) = ( 2 )
➡ ( 2πr³ )/3 = ( 2/3 )πR³
➡ => r³/R³ = ( 2/3 )/( 2/3 )
➡ => ( r/R )³ = 1/1
❥r : R = 1 : 1
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