A spherical shell of internal and external diameter 6cm and 10cm respectively is melted and recast i...........

Quantitative Aptitude ( CCS) Mensuration 3D

A spherical shell of internal and external diameter 6cm and 10cm respectively is melted and recast into a cylinder of diameter 14 cm. find the height of the cylinder ?

3.687 cm

2.666 cm

2.587 cm

none of these

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Explanation:

Internal diameter of a hollow spherical shell =6 cm
Internal radius of a hollow spherical shell = 3 cm
External diameter of a hollow spherical shell = 10 cm
External radius of a hollow spherical shell = 5 cm
Volume of the spherical shell = (4/3)∏×(5³−3³)…………….(i)
Diameter of the cylinder = 14 cm
Radius of the cylinder = 7cm
Let the height of the cylinder be (x) cm
Volume of the cylinder = ∏×7²×X………..(ii)
According to the question,
Volume of the cylinder is equals to the volume of the spherical shell.
(4/3)∏×(5³−3³)=49 *x
X= 2.666 cm