Water drips from a tap at the rate of 4 drops every 3 seconds volume of one drop of water is 0.4 cm cube that if water is collected in a cylindrical vessel. the diameter and uniform thickness of this vessel is 10 centimetre and 1cm respectively how much minutes will be required to fill the vessel completely if its height is 70 cm
Answers
Answer:
(1) 11 mins (2) 20 vessels
Step-by-step explanation:
Find the volume of the tank:
Volume = πr²h
Volume = π(8 ÷ 2)²(7) = 352 cm³
Find the number of droplet needed to fill the tank:
1 droplet = 0.4 cm³
Number of droplets = 352 ÷ 0.4 = 880
Find the time needed for 880 droplets:
4 droplets = 3 seconds
1 droplet = 3 ÷ 4 = 3/4 seconds
880 droplets = 3/4 x 880 = 660 seconds
Find the time in mins:
60 seconds = 1 min
660 seconds = 660/60 min = 11 mins
Find the number of droplets filled in 3 hours 40 mins
3 hours 40 mins = 3 x 60 + 40 mins = 220 mins
11 mins = 880 droplets
1 min = 880 ÷ 11 = 80 droplets
220 mins = 80 x 220 = 17600 droplets
Find the number of vessels:
1 vessel = 880 droplets
Number of vessels = 17600 ÷ 880 = 20 vessels
Answer: (1) 11 mins (2) 20 vessels
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220 minutes will be required to fill the vessel completely if its height is 70 cm.
Step-by-step explanation:
The volume of each drop is 0.4 cm³
The tap drip at a rate of 4 drops per 3 seconds
The volume of water coming at 1 second is:
0.4/3 × 4 = 1.6/3 cm³
Let the height of the vessel is h = 7 cm
Let the diameter of the vessel is 2r = 8 cm i.e r = 4 cm
The volume of the cylindrical vessel is given by the formula:
V = πr²h
On substituting the values, we get,
V = 22/7 × (4)² × 7
∴ V = 16 × 22 cm³
Let the time taken to fill the vessel be 'x'
Volume of the water coming at x seconds = Volume of the cylindrical vessel
1.6/3 x = 16 × 22
x = (16 × 22 × 3)/1.6 = 660 seconds
Now,
x = 660/60 = 11 minutes
The time taken to fill the cylindrical vessel is 11 minutes.
3 hours 40 minutes = 3 × 60 + 40 = 180 + 40 = 220 minutes