a social welfare association decides to subtitling water for the flood affected people the drinking water is filled in a water tanker which is in the shape of a cylinder with hemispherical ends as shown in the figure the whole length of the tank is 4.2 metre and the diameter of the base cylinder and two hemispheres are its 1.2 metre if the distributor giving water to 60 people in a container which is in the shape of a cylinder of radius 21 cm and height 15 cm find the quantity of water left in the tanker after distribution in letter used by is equal to 22 by 7
Answers
The quantity of water left in the tanker after distribution in litres is 3047.6 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 = 15 cm = 0.15 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 * 0.15
= 1.2474 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 - 1.2474 m³
= 3.0476 m³
∵ 1 m³ = 1000 litres
= 3047.6 litres
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