A hemispherical tank of radius 2.1m is full of water. It is connected with a pipe which empties it at the rate of 7 litres per second. How much time will it take to empty the tank completely?
Answers
Given:
The radius of the tank=2.1m
The rate of pipe=7 l/s
To find:
The time that is taken to empty the tank completely
Solution:
The pipe empties the tank completely in 2771 seconds.
We can find the time by following the given steps-
We know that the tank is hemispherical in shape.
So, the total amount of water in the tank is equal to its volume.
The volume of the hemispherical tank=2/3π, where r is the radius of the tank.
It is given to us that the radius of the tank is 2.1m.
On putting the value of r, the volume is
=2/3π×2.1×2.1×2.1
=2/3×22/7×21/10×21/10×21/10
=22×21×21/500
=19.40
Now, we know that 1=1000 litres.
So, the volume of the tank=19.40×1000
=19400l
The pipe connected with the tank empties it at the rate of 7 l/s.
The time that is taken by the pipe to empty the tank completely=Volume of tank/ rate of pipe emptying the tank
On putting the values, we get
=19400/7
=2771 seconds
Therefore, the pipe empties the tank completely in 2771 seconds.
Given:
Radius of tank =2.1 m
Rate at which tank is emptied = 7 litres per second
To Find:
Time will it take to empty the tank completely
Step-by-step explanation:
Radius of the hemisphere = 2.1 m = 210 cm
∴ Volume of the hemisphere
2/3 ×π × 210 ×210 ×210cm ³
The cylindrical pipe empties it at the rate of 7 litres ie, 7000cm ³ of water per second.
Hence, the required time to empty the tank
= (2/3 × 22/7 × 210 × 210 ×210 ÷ 7000)
= 2771 seconds
Answer = 2771 seconds