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Question
The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.
Solution
Inner radius of hollow cylinder r1 = 15 cm
Outer radius of hollow cylinder r2 = 20 cm
The volume of hollow cylinder `= pi (r_2^2 - r_1^2) h`
Since,
The hollow cylinder is melted and recast into a solid cylinder of same height.
Let r be the radius of solid cylinder.
Therefore,
The volume of solid cylinder = volume of hollow cylinder.
`pir^2 h = pi (r_2^2 - r_1^2) h`
`r^2 = (20^2 - 15^2)`
`r^2 = 35 xx 5`
`r = 13.2 cm`
Hence, the radius of solid cylinder is13.2 cm .
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