44. A hemispherical bowl of internal diamet36 cm contains liquid. This

1.	44. A hemispherical bowl of internal diamet36 cm contains liquid. This liquid is filleinto 72 cylindrical bottles of diamete6 cm. Find the height of each bottie, if IOliquid is wasted in this transfer
Answer» Given : Diameter of hemispherical bowl = 36 cm , So radius of hemispherical bowl, r = diameter/2 = 18 cm And we know Volume of hemisphere =2πr^3/3, So Volume of hemispherical bowl =23πr^3=23π(18)^3cm^3 And ,now, the liquid is transferred into 72 bottles and 10% liquid is wasted in this transfer.So,volumeofliquidthatistransferred=23π(18)^3−10/100×23π(18)^3=910×23π(18)^3cm^3 Given diameter of each cylindrical bottle = 6 cm , So radius , R = 3 cmAnd let the height of each bottle = h cmWe know volume of cylinder =πR^2h, So we get72(πR^2h)=910×23π(18)^3⇒72×π×(3)^2×h=910×23π(18)^3⇒h=5.40cmSo,Height of each cylindrical bottle =5.40 cm

44. A hemispherical bowl of internal diamet36 cm contains liquid. This liquid is filleinto 72 cylindrical bottles of diamete6 cm. Find the height of each bottie, if IOliquid is wasted in this transfer

Answer»

Given : Diameter of hemispherical bowl = 36 cm , So radius of hemispherical bowl, r = diameter/2 = 18 cm

And we know Volume of hemisphere =2πr^3/3, So

Volume of hemispherical bowl =23πr^3=23π(18)^3cm^3

And ,now, the liquid is transferred into 72 bottles and 10% liquid is wasted in this transfer.So,volumeofliquidthatistransferred=23π(18)^3−10/100×23π(18)^3=910×23π(18)^3cm^3

Given diameter of each cylindrical bottle = 6 cm , So radius , R = 3 cmAnd let the height of each bottle = h cmWe know volume of cylinder =πR^2h, So we get72(πR^2h)=910×23π(18)^3⇒72×π×(3)^2×h=910×23π(18)^3⇒h=5.40cmSo,Height of each cylindrical bottle =5.40 cm

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