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Question
A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
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Solution
Inner diameter of the bowl = 30 cm
Inner radius of the bowl `=(30 "cm")/2= 15 "cm"`
Volume of liquid `= 2/3pir^3 =2/3xxpixx15^3 "cm"^3`
Radius of each bottle = 2.5 cm
Height = 6 cm
Volume of each bottl `=pir^2h = pixx5/2xx5/2xx6=(75pi)/2 "cm"^3`
total number of bottles required `=[(2/3pixx15xx15xx15xx6)/((75pi)/2)]= (2pixx15xx15xx15xx2)/(3xx75pi) = 15xx14=60`
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