a social welfare Association decide to supply drinking water for flood affected people.the drinking water id filled in a water tanker which is in the shape of a cylinder with hemisphere end ss shown in fig the whole length of the tanker is 4:2 meter n the diameter of base of the cylinder n two hemisphere are each 1:2 m.if they distrribute drinking water to 60 people in a container.each is the shape of s cylinder of raduis 21 cm n height 50 cm find the quantity of water leftbin the tankers after distribution in ltr use π=22/7
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 m³
∵ 1 m³ = 1000 litres
= 137 litres
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