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# A metallic spherical shell of internal and external diameter 4 cm and 8 cm respectively, is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone isA. 12 cmB. 14 cmC. 15 cmD. 8 cm

Given: Metallic spherical shell of internal and external diameter 4 cm and 8 cm respectively

Recast into the form of a cone of base diameter 8 cm.

Volume of spherical shell is : × π × [(r1)3 — (r2)3] (here r1 an r2 are External and internal radii respectively)

Let v1 be the volume of given Spherical shell.

v1 = × π × [( )3 — ( )3] = × π × [(4)3 — (2)3] = × π × [64 — 8] = × π × 56 cm3

Volume of the cone is given by : × π × r2 × h

Let v2 be the volume of cone.

V2 = × π × ( )2 × h = × π × 16 × h cm3

We know that when a object is moulded from one shape to other its volume does not change.

v1=v2

That is, × π × 56 = × π × 16 × h

h = = = 14

h = 14cm

That is, height of the cone = 14cm

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