A solid right circular cylinder as a base radius of 12 cm and height 16cm it is melted and made into 16 spherical balls of equal size .find radius of each ball
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Radius of right circular cylinder ( R ) = 12 cm.
Height of right circular cylinder ( H ) = 16 cm.
Volume of right circular cylinder = πr²H = 22/7 × 12 × 12 × 16 = ( 22 × 144 × 16 / 7 ) = ( 50688/7 ) = 7241.14 cm².
Volume of spherical balls = 4/3 πR³
It is given that the right circular cylinder is melted and made into 16 spherical balls. it means ,
Volume of cylinder = Volume of spherical balls.
7241.14 = 4/3 πR³
πR³ = ( 7241.14 × 3 ) / 4
22 / 7 × R³ = ( 7241.14 × 3 /4 )
R³ = ( 7241.14 × 3 × 7 / 22 × 4 )
R³ = ( 152063.94 / 88 )
R³ = 1727.99
R = ³√1727.99 cm
Height of right circular cylinder ( H ) = 16 cm.
Volume of right circular cylinder = πr²H = 22/7 × 12 × 12 × 16 = ( 22 × 144 × 16 / 7 ) = ( 50688/7 ) = 7241.14 cm².
Volume of spherical balls = 4/3 πR³
It is given that the right circular cylinder is melted and made into 16 spherical balls. it means ,
Volume of cylinder = Volume of spherical balls.
7241.14 = 4/3 πR³
πR³ = ( 7241.14 × 3 ) / 4
22 / 7 × R³ = ( 7241.14 × 3 /4 )
R³ = ( 7241.14 × 3 × 7 / 22 × 4 )
R³ = ( 152063.94 / 88 )
R³ = 1727.99
R = ³√1727.99 cm
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