A social welfare association decides to apply drinking water for the food accepted people.The drinking water tanker which is in the shape of cylinder with hemispherical end.The whole height of the tanker is 4.2m and the diameter of base of the cyclinder and two hemispherical are each 1.2m. If they distribute drinking water to 60 people in a container each is in the shape of a cylinder of radius 21cm and height 50cm,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 small 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 small 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 m^3
∵ 1 m³ = 1000 litres
= 137 litres
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