A metallic spherical shell of internal and external

Asked by admin @ 29/08/2021 in Math viewed by 305 People

Q2. 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 (A) 12cm (B) 14cm (C) 15cm (D) 18cm

Answered by admin @ 29/08/2021

If the metallic spherical shell is recast , the volume of the metal remains constant always.

So , the volume of metal in the spherical shell = Volume of the cone formed

Volume of the metal in the metallic spherical shell = Volume of Outer sphere - Volume of inner sphere
This is because the metal is only present in between the inner and outer spheres.
radius of inner sphere = 4/2 = 2 ; radius of outer sphere = 8/2 = 4
radius of cone = 8/2 = 4

So , volume of metal = $\frac{4}{3}* \pi * R^{3}- \frac{4}{3} * \pi * r^{3}$
Where ,R=radius of outer sphere
r = radius of inner sphere

So,V = (4/3)* $\pi *( 4^{3} - 2^{3})$

Equating this to volume of cone which is (1/3)* $\pi$ * $r^{2} *h$

SO,(4/3)*pi * (64-8) = (1/3)*pi * 16 * h

h = 14 cm

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A metallic spherical shell of internal and external

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