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Question
A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?
Solution
Internal radius of hemispherical bowl r = 15 cm
The volume of bowl `= 2/3 pir^3`= volume of liquid
`= 2/3 pi(15)^3`
Volume of liquid = 2250 π cm3
Since, the liquid filled into the cylindrical shaped bottles of radius `5/2 cm`and height 6 cm.
Let n be the no. of bottles.
Therefore,
The volume of liquid = n × volume of cylindrical shaped bottle
`2250pi = n xx pi xx (5/2)^2 xx 6`
`2250 = n xx 25 / 4 xx 6`
`n = (2250 xx 4)/(25 xx 6)`
` n = 60`
Hence, the no. of bottles = 60
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