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# The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

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Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.1 mensuration.

we have to find find the height of the cylinder given that the
diameters of the internal and external surfaces of a
hollow spherical shell are 6 cm and 10 cm respectively. If it is melted
and recast into a solid cylinder of diameter 14 cm.

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1. Given,

Internal diameter of hollow spherical shell = 6 cm

So, the internal radius of hollow spherical shell = 6/2 = 3 cm = r

External diameter of hollow spherical shell = 10 cm

So, the external diameter of hollow spherical shell = 10/2 = 5 cm = R

Diameter of the cylinder = 14 cm

So, the radius of cylinder = 14/2 = 7 cm

Let the height of cylinder be taken as h cm

Then, according to the question we have

Volume of cylinder = Volume of spherical shell

π × r2 × h = 4/3 π × (R3 – r3)

π × 72 × h = 4/3 π × (53 – 33)

h = 4/3 x 2

h = 8/3 cm

Therefore, the height of the cylinder = 8/3 cm

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