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Question
How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?
Solution
Vcyl = πr2h
Small Cylinders
r = 2 cm, h = 3 cm
∴ `"V"_"small" = pi"r"^2"h"`
`= pi xx 2 xx 2 xx 3` ...(i)
Big Cylinders
d = 12 cm, r' = `12/2` = 6 cm
h' = 15 cm
∴ `"V"_"big" = pi"r'"^2"h'"`
`= pi xx 6 xx 6 xx 15` ...(ii)
`n = "V"_"big"/"V"_"small"` ...[From (i) and (ii)]
`= (pi xx 6 xx 6 xx 15)/(pi xx 2 xx 2 xx 3)`
= 45
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