social welfare Association decides to supply drinking water for the flood affected people the drinking water is filled in a water tanker which is in the shape of cylinder with hemispherical and as shown in the figure the whole length of the tanker is 4.2 metre and diameter of the base of the cylinder and two hemisphers are each 1.2 metre if their distribute drinking water to 60 people in a container is in the shape of cylinder of radius 21 cm and height 50 find the quantity of water left in tanker after distribution in litres
Answers
Given : A water container cylindrical with two hemispherical ends . to distribute Drinking water for 60 people
To find : Water left in Tank
Solution:
Length of Tanker is 4.2 m
Radius of base of cylinder = hemisphere = Diameter/2 = 1.2/2 = 0.6 m
Length of each hemisphere = 0.6 m
Length of cylindrical part = 4.2 - 0.6 - 0.6 = 3 m
Volume of Cylinder = π r²h
= π (0.6)² * 3 m³
Volume of two hemisphere = 2 * (2/3)π r³
= (4/3) π (0.6)³
= 0.8 π (0.6)² m³
Total Volume = 3.8 π (0.6)² m³
= 1.368 π m³
Volume of one container = π (21/100)² * (50/100) m³
= π (.21)² / 2 m³
Volume of 60 container = 60 * π (.21)² / 2 m³
= 30 π (.21)² m³
= 1.323 π m³
Water left in Tank = 1.368 π - 1.323 π = 0.045 π m³
= 0.045 π m³
= 0.141 m³
1 m³ = 1000 litre
=> 0.141 m³ = 141 Litre
141 litre water left in Tank
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Answer:
Quantity of water left in the tanker = 1,499 litters
Step-by-step explanation:
The quantity of water left in the tanker after distribution = Total quantity - Distributed quantity
Total quantity = Volume of the tanker
Volume of the cylinder of 4.2 m length and 1.2 m of a diameter.
Volume of cylinder = π r² L
(given L = 4.2m and diameter = 1.2m)
Substituting, we get Volume (cylinder) = 22/7 * 0.6 * 0.6 * 4.2 = 4.752 m³
Volume of 2 hemispheres at the end = 2* 2πr³/3 = 4 * 22/7 * (0.6)³ / 3 = 792 / 875 m³
Volume of tanker = 4.752 + 792/875 = 5.657 m³
Distributed quantity = 60 times the volume of a cylinder of radius 21 cm and height is 50 cm
= 60 * πr²L
= 60 * 22/6 * 21² * 50
= 4,158,000 cm³
= 4.158 m³
The quantity of water left in the tanker after distribution = 198/35 - 4.158 = 1.499 m³
1 m³= 1,000 litter
So quantity of water left in the tanker after distribution = 1.499 * 1000 = 1499 litters
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