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प्रश्न
The dimensions of a solid iron cuboid are 4·4 m × 2·6 m × 1·0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe
उत्तर
Let the length of the pipe be h cm.
Volume of the solid iron cuboid = 4·4 m × 2·6 m × 1·0 m = 440 cm×260 cm×100 cm
Internal radius of the pipe, r = 30 cm
External radius of the pipe, R = 30 + 5 = 35 cm
Volume of iron in the pipe = `piR^2h - pir^2h = pih(R^2 - r^2)`
`= pih(35^2 - 30^2)`
`= pih(35 - 30)(35 + 30)`
`= pih(5 xx 65)`
Volume of iron in the pipe = Volume solid iron cuboid
`=> pih(5 xx 65) = 440 xx 260 xx 100`
`=> h = (440 xx 260 xx 100 xx 7)/(5 xx 65 xx 22)`
`=> h = 11200 cm = 112m`
Hence, the length of the pipe is 112 m.
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