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Question
A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?
Solution
The internal radius of the hemispherical bowl is 9cm. Therefore, the volume of the water in the hemispherical bowl is
`V = 2/3 pi xx (9)^3 cm^3`
The water in the hemispherical bowl is required to transfer into the cylindrical bottles each of radius`3/2`cm and height 4cm. Therefore, the volume of each of the cylindrical bottle is
`V_1 = pi xx(3/2)^2 xx 4 cm^3`
Therefore, the required number of cylindrical bottles is
`V = (2/3 pi xx (9)^3)/( pi xx(3/2)^2 xx 4)`
` = (2 xx (9)^3 xx (2)^2)/(3 xx (3)^2 xx 4)`
`= 54`
Hence No. of bottles = 54.
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