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Question
A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied in a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.
Solution
Let the height of water in the cylindrical vessel be h cm.
Given: Radius of the hemispherical bowl, r = 9 cm
∴ Volume of the water in hemispherical bowl, `V_1=pi2/3r^3`
`V_1=pi2/3xx(9cm)`
Given: Radius of the cylinder, R = 6 cm,
∴ Volume of water in the cylindrical vessel, V2 = π r2h
⇒ V2 = π (6 cm)2 h
Since water is emptied from the hemispherical bowl into the cylindrical vessel,
∴Volume of water in cylindrical vessel = Volume of the water in hemispherical bowl
`rArrpi(6)^2h=2/3pi(9)^3`
`rArrh=(2xx(9)^3)/(3xx(6)^2)`
`rArrh=27/2`
`rArrh=13.5`
Thus, the height of water in the cylindrical vessel is 13.5 cm.
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