Q. 325.0( 1 Vote )

A. 12 cm

B. 14 cm

C. 15 cm

D. 8 cm

Answer :

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 × [(r_{1})^{3} — (r_{2})^{3}] (here r_{1} an r_{2} are External and internal radii respectively)

Let v_{1} be the volume of given Spherical shell.

∴ v_{1} = × π × [()^{3} — ()^{3}] = × π × [(4)^{3} — (2)^{3}] = × π × [64 — 8] = × π × 56 cm^{3}

Volume of the cone is given by : × π × r^{2} × h

Let v_{2} be the volume of cone.

∴ V_{2} = × π × ()^{2} × h = × π × 16 × h cm^{3}

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

∴ v_{1}=v_{2}

That is,

× π × 56 = × π × 16 × h

h = = = 14

∴ h = 14cm

That is, height of the cone = 14cm

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