Wine from a full cylindrical container with a diameter of 11 cm and a height of 17 cm is poured into glasses that have the shape of a hemisphere with a diameter of 9 cm.
(i) How many glasses can be filled completely?
(ii) How many liters of wine needed for 50 full glasses?
Answers
Given : Wine from a full cylindrical container with a diameter of 11 cm and a height of 17 cm is poured into glasses that have the shape of a hemisphere with a diameter of 9 cm.
To Find :
(i) How many glasses can be filled completely?
(ii) How many liters of wine needed for 50 full glasses?
Solution:
Radius = Diameter /2
Volume of cylinder = πr²h
r = 11/2 h = 17
=> Volume of cylindrical container = π ( 11/2)² * 17 = 2057 π/8
Volume of hemisphere = (2/3)πr³
r = 9/2
=> Volume of glass = (2/3)π(9/2) ³ = 486 π/8
glasses can be filled completely ≤ (2057 π/8) / (486 π/8)
≤ 4.23
= 4
Hence 4 glasses can be filled
wine needed for 50 glasses = 50 * 486 π/8
= 9,542 cm³
= 9.542 Litre
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