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**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 8cm. The height of the cone is**

Answer:

14cm

Volume of spherical shell = Volume of cone recast by melting

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= 4/3 π (r_{2}^{3} – r_{1}^{3})

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

volume of given shell = 4/3 π (4^{3} – 2^{3})

= 4/3 π (56)

= (224/3) π

We know that,

Volume of cone = 224π /3 cm^{3}

For cone,

Base diameter = 8 cm

Base radius, r = 4 cm

Let Height of cone = ‘h’.

We know,

Volume of cone = (1/3) π r^{2}h,

Where r = Base radius and h = height of cone

Volume of given cone = (1/3) π 4^{2}h

⇒ 224π /3 = 16πh /3

⇒ 16h = 224

h = 14 cm

**So, Height of cone is 14 cm.**

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