A farmer connects a pipe of internal diameter 0.2 m from a canal into a cylindrical tank in his field,
which is 10m in diameter and 3.5m deep. If water flows through the pipe at the rate of 2.5 km/hr, in how much
time will the tank be filled. After filling the tank completely, he empties it by watering the field of dimension
50m × 44m × hm. Find the height of water level in the field.
Answer:
Radius of the cylinder = 14 m
Radius of the base of the cone = 14 m
Height of the cylinder (h) = 3 m
Total height of the tent = 13.5 m
Surface area of the cylinder
=2πrh=(2×22/7×14×3) m2=264 m2
Height of the cone
=Total height – Height of cone = (13.5-3) m=10.5 m
Surface area of the cone = πr√r2+h2
=πr√r2+h2=(227×14×√142+10.52) m2
Total surface area
=(264+770) m2=1034 m2
∴ Cost of cloth=Rs 1034×80=Rs 82720
Answer:
Statement of the given problem,
A farmer connects a pipe of internal diameter (20 cm = 20/100 =) 0.2 m from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of (4 km/hr = 4*5/18 =) 10/9 m/s, in how much time will the tank be filled completely?
Let T denotes the time (in hrs) that will be required to fill the tank.
From above mentioned given data we get as follows,
T = (Volume of tank: L) / (Volume flow of water: L/s)
or T = [2*(10/2)^2*π] / [(10/9)*(0.2/2)^2*π]
or T = 2*25*9 / 10*.01 = 4500 (s) = (5/4 hrs =) 1 hr 15 min [Ans]