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Question
A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.
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Solution
Internal diameter of the bowl = 36 cm
Internal radius of the bowl, r = 18 cm
Volume of the liquid, V =(2/3)๐r3 =(2/3)× ๐ × 183
Let the height of the small bottle be ‘h’.
Diameter of a small cylindrical bottle = 6 cm
Radius of a small bottle, R = 3 cm
Volume of a single bottle = ๐R2h = ๐ × 32 × h
No. of small bottles, n = 72
Volume wasted in the transfer =(10/100)×(2/3)× ๐ × 183
Volume of liquid to be transferred in the bottles
`=2/3xxpixx18^3-10/100xx2/3xxpixx18^3`
`=2/3xxpixx18^3(1-10/100)`
`=2/3xxpixx18^3xx90/100`
we know that volume of cylinder =`pir^2h` so we get
`72(pir^2h)=(2/3xxpixx18^3xx90/100)`
`72=(2/3xxpixx18^3xx90/100)/(pixx3^2xxh)`
`72=(2/3xx18^3xx9/10)/(3^2xxh)`
`h=(2/3xxpixx18xx18xx18xx9/10)/(pixx3^2xx72) `
h=5.4 cm
Height of the small cylindrical bottle = 5.4 cm
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