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Question
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.
Solution
We have,
the internal base radius of spherical shell, r1 = 3 cm,
the external base radius of spherical shell, r2 = 5 cm and
the base radius of solid cylinder , r = 14/2 = 7 "cm".
Let the height of the cylinder be h.
As,
Volume of solid cylinder = volume of spherical shell
`rArr pir^2h = 4/3 pir_2^3 - 4/3pir_1^3`
`rArr pir^2h = 4/3pi(r_2^3 - r_1^3)`
`rArr r^2h =4/3 (r_2^3 - r_1^3)`
`rArr 7xx7xxh = 4/3(5^3-3^3)`
`rArr 49xx h =4/3(125-27)`
`rArr h = 4/3xx98/49`
`therefore h = 8/3 "cm"`
So, the height of the cylinder is `8/3` cm.
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