A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone ...........

Quantitative Aptitude ( CCS) Mensuration 3D

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. What is the height of the cone ?

12 cm

14 cm

17 cm

18 cm

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Explanation:

Given, internal diameter of hollow sphere = 4 cm, then internal radius (r) = 2 cm
And, external diameter of hollow sphere = 8 cm, then external radus (R) = 4 cm
Diameter of cone = 8 cm, then radius of cone (r₁) = 4 cm
Let height of cone = h
Note : When an object is melted and given a different shape, the volumes of both the objects (of two different shapes) remain equal.
∴ Volume of cone = Volume of hollow sphere