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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 ?


Options:
A .  42.3215 cm
B .  44.0123 cm
C .  44.0625 cm
D .  44.6023 cm
Answer: Option C

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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