Question

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:​

Answer 1

${\huge{\underline{\underline{\mathfrak{\green{Solution:-}}}}}}$

❥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

⠀⠀⠀⠀⠀⠀

⠀$♡ThankYou♡$