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Question
A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.
Solution
We have,
the radius of the hemispherical bowl, R=9 cm and
the internal base radius of the cylindrical vessel, be h.
As,
Volume of water in the cylindrical vessel=Volume of hemispherical bowl
`rArr pir^2h = 2/3piR^3`
`rArr r^2h = 2/3 R^3`
`rArr 6xx6xxh=2/3xx9xx9xx9`
`rArr "h" =2/3 xx (9xx9xx9)/(6xx6)`
`rArr "h" = 27/2`
`rArr "h" =27/2`
∴ h=13.5 cm
so,the height of the water in the cylindrical vessel is 13.5 cm.
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