Q. 25

Answer :

Height of metallic cylinder = h = 5 cm

Radius of metallic cylinder = r = 3 cm

Volume of solid cylinder = πr^{2}h

= π × 3 × 3 × 5 cm^{3}

= 45π cm^{3}

Height of conical hole = h’ = 8/9 cm

Radius conical hole = r’ = 3/2 cm

Volume of conical hole = 1/3 πr’^{2}h’

= 1/3 × π × 3/2 × 3/2 × 8/9 cm^{3}

= 2/3 π cm^{3}

Volume of metal left in cylinder = Volume of metallic cylinder – Volume of conical hole

Volume of metal left in cylinder = 45π - 2/3 π = 133π/3

Ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape = Volume of metal left in cylinder/ Volume of conical hole

Volume of metal left in cylinder : Volume of conical hole = 133π/3 : 2/3 π

Volume of metal left in cylinder: Volume of conical hole = 133: 2

Ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape is 339:4

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