Q. 9

# A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8 cm. The height of the cone is

A. 12 cm

B. 14 cm

C. 15 cm

D. 18 cm

Answer :

Volume of spherical shell = Volume of cone recast by melting [1]

For Spherical Shell,

Internal diameter, d_{1} = 4 cm

Internal radius, r_{1} = 2 cm

[ as radius = 1/2 diameter]

External diameter, d_{2} = 8 cm

External radius, r_{2} = 4 cm

Now,

As volume of spherical shell

where r_{1} and r_{2} are internal and external radii respectively.

volume of given shell

Using [1] we have

Volume of cone = 224π /3 cm^{3}

__For cone,__

Base diameter = 8 cm

Base radius, r = 4 cm

[ as radius = 1/2 diameter]

Let Height of cone be 'h'.

As,

volume of cone =

where r = Base radius and h = height of cone

Volume of given cone

⇒ 16h = 224

h = 14 cm

So, Height of cone is 14 cm.

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