a social welfare Association decides to supply drinking water for the flood affected people the drinking water is filled in water tanker which is in the shape of cylinder with hemispherical end and the whole length of the tanker is 4.2 metre and the diameter of the base of the cylinder and the two hemisphere are each of 1.2 M if the distribute drinking water to 60 people in a container each is in the shape of cylinder of radius 21 cm and height 50 cm find the quantity of water left in the tanker after distribution in litre
Answers
The quantity of water left in the tanker after distribution in litres is 137 litres.
Step-by-step explanation:
Step 1:
The length of the water tank = 4.2 m
The diameter of the base of the cylinder and the two hemispherical ends, d = 1.2 m
So, the radius, r = d/2 = 1.2/2 = 0.6 m
∴ The length of the cylindrical portion of the tank, h = 4.2 - 1.2 = 3 m
Now,
The volume of the cylindrical portion is,
= πr²h
= × 0.6² × 3
= 3.39 m³
and
The volume of the 2 hemispherical ends is,
= 2 × [ πr³]
= × × 0.6³
= 0.905 m³
∴ The volume of the drinking water tank is given by,
= [ volume of the cylindrical portion] + [volume of the 2 hemispherical ends]
= 3.39 m³ + 0.905 m³
= 4.295 m³
Step 2:
The dimension of the cylindrical containers:
Radius, r = 21 cm = 0.21 m
Height, h = 50 cm = 0.5 m
The no. of people to whom the drinking water was distributed in such containers = 60
∴ The volume of water distributed to 60 people is given by,
= 60 * [Volume of the small cylindrical containers]
= 60 * [πr²h]
= 60 * (22/7) * 0.21² * 0.5
= 4.158 m³
Step 3:
Therefore,
The quantity of water left in the tanker after the distribution is given by,
= [volume of the drinking water tank] – [volume of water distributed to 60 people]
= 4.295 m³ - 4.158 m³
= 0.137 m³
∵ 1 m³ = 1000 litres
= 137 litres
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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