A hemispherical bowl of internal diameter 36 em contains liquid. Thisl

1.	A hemispherical bowl of internal diameter 36 em contains liquid. Thisliquid is filled into 72 cylindrical bottles of diameter 6 em. Find the heightof the each bottle, if 10% liquid 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 =2/3πr^3=2/3π18^3cm^3And ,now, the liquid is transferred into 72 bottles and 10% liquid is wasted in this transfer.So,volumeofliquidthatistransferred=2/3π18^3-10/100×2/3π18^3=9/10×2/3π18^3cm^4 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 get72πR^2h=9/10×2/3π18^3⇒72×π×32×h=9/10×2/3π18^3⇒h=5.40cmSo,Height of each cylindrical bottle =5.40 cm ( Ans )

A hemispherical bowl of internal diameter 36 em contains liquid. Thisliquid is filled into 72 cylindrical bottles of diameter 6 em. Find the heightof the each bottle, if 10% liquid 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 =2/3πr^3=2/3π18^3cm^3And ,now, the liquid is transferred into 72 bottles and 10% liquid is wasted in this transfer.So,volumeofliquidthatistransferred=2/3π18^3-10/100×2/3π18^3=9/10×2/3π18^3cm^4

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 get72πR^2h=9/10×2/3π18^3⇒72×π×32×h=9/10×2/3π18^3⇒h=5.40cmSo,Height of each cylindrical bottle =5.40 cm ( Ans )

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