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प्रश्न
Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels.
उत्तर
The volume of 1st cylindrical vessel `= pi xx (15)^2 xx 20`
`= 225 xx 20 xx pi`
`= 4500pi cm^2`
The volume of 2nd cylindrical vessel `= pi xx (12)^2 xx 16`
`= 144 xx 16 xx pi`
`= 1304pi cm^3`
Let r be the radius of vessel, which will just contain oil of the both vessels.
Therefore,
Volume of cylindrical vessel = sum of the volume of both vessels.
i.e.,
`pir^2 h = 4500pi + 2304 pi`
`pir^2 xx 21 = 6804 pi`
`r^2 = (6804)/21`
`r^2 = 324`
`r = 18cm`
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