Important problem from the cbse board exam point of view; becuse last time this problem was asked in 2012. Problem from RS Aggarwal book, problem number 5, page number 809, exercise 17B, chapter volume and surface area of solid.

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# The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.

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Given data,

The internal base radius of spherical shell, r1 = 3 cm,

the external base radius of spherical shell, R = 5 cm

the base radius of solid cylinder, r = 14/2 = 7 cm

Volume of the spherical shell = Volume of the cylinder

[4/3] π [ R³ – r1³ ] = π r² h

[4/3] [ R³ – r1³ ] = r² h

[4/3] [ 5³ – 3³ ] = [ 7² ] * h

( [4/3] * 98 ) / 49 = h

h= 8/3

∴ The height of the cylinder is 8/3cm