Question
What length of solid cylinder 2 cm in diameter mush be taken to cast into a hollow cylinder of external diameter 12 cm , 0.25 thick and 15 cm long ?
Answer: Option C
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External radius = 6 cm, Internal radius = (6 - 0.25) cm = 5.75 cm.
Volume of material in hollow cylinder.
= ` { 22/7 xx [(6)^2 - (5.75)^2] xx 15} cm^3`
=` (22/7 xx 11.75 xx 0.25 xx 15) cm^3`
= `(22/7 xx 1175/100 xx 25/100 xx 15) cm^3`
= `((11 xx 705)/(56)) cm^3`
Let the length of solid cylinder be h . Then,
`22/7 xx 1 xx 1 xx h = ((11 xx 705)/(56))`
`hArr h = ((11 xx 705)/(56) xx 7/22) ` cm = 44.0625 cm.
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