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प्रश्न
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?
उत्तर
External diameter of hollow cylinder = 20 cm
Therefore, radius = 10 cm
Thickness = 0.25 cm
Hence, Internal radius = (10 – 0.25) = 9.75 cm
Length of cylinder (h) = 15 cm
∴ Volume = πh(R2 – r2)
= π × 15(102 – 9.752)
= 15π(100 – 95.0625) cm3
= 15π × 4.9375 cm3
Diameter = 2 cm
Therefore, radius (r) = 1 cm
Let h be the length
Then, volume = πr2h = π(1 × 1)h = πh
Now, according to given condition:
πh = 15π × 4.9375
`=>` h = 15 × 4.9375
`=>` h = 74.0625
Length of cylinder = 74.0625 cm
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