A metallic cylinder has radius 3 cm and height 5 cm. To reuse its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of 3/2 cm and its depth is 8/9 cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
Height of metallic cylinder = h = 5 cm
Radius of metallic cylinder = r = 3 cm
Volume of solid cylinder = πr2h
= 3.14 × 3 × 3 × 5 cm3
= 141.3 cm3
Height of conical hole = h’ = 8/9 cm
Radius conical hole = r’ = 3/2 cm
Volume of conical hole = 1/3 πr’2h’
= 1/3 × 3.14 × 3/2 × 3/2 × 8/9 cm3
= 2.1 cm3
Volume of metal left in cylinder = Volume of metallic cylinder – Volume of conical hole
Volume of metal left in cylinder = 141.3 cm3 – 2.1 cm3
= 139.2 cm3
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 = 139.2 : 2.1
Volume of metal left in cylinder: Volume of conical hole = 464 : 7
Ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape is 464:7