The diameters of the internal and external surfaces of a hollow spherical shell are 10cm and 6 cm re...........

Quantitative Aptitude ( CCS) Mensuration 3D

The diameters of the internal and external surfaces of a hollow spherical shell are 10cm and 6 cm respectively. If it is melted and recasted into a solid cylinder of length 8/3 cm, find the diameter of the cylinder.

28√2 cm

14√2 cm

26√2 cm

18√2 cm

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Explanation:

External diameter of a sphere = 10 cm
Internal diameter of the sphere = 6 cm
Volume of the sphere = 4/3 π (R³ – r³)
= (4/3) (22/7) (10³ – 6³)
= (4/3) (22/7) (784)
= 9856 / 3 cm³
Height of the cylinder formed = 8/3 cm
Let the radius of the cylinder be ‘r’ cm
Volume of the cylinder = πr²h
= 22/7 * r² * 8/3
= 22/7 * r² * 8/3 = 9856 / 3
r² = 392
r = 14√2 cm
So Diameter of the cylinder = 2 x 14√2 =28√2 cm