A cylindrical water tank, with diameter 2.8 m and height 4.2 m, is filled in by apipe of diameter 7 cm, through which water flows at the rate of 4 m/sec.How many minutes will it take for the pipe to completely fill the tank?(Take 227π = )
Question
A cylindrical water tank, with diameter 2.8 m and height 4.2 m, is filled in by apipe of diameter 7 cm, through which water flows at the rate of 4 m/sec.How many minutes will it take for the pipe to completely fill the tank?(Take 227π = )
Solution
Sure, let's solve this step by step.
Step 1: Calculate the volume of the cylindrical tank. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. The radius is half the diameter, so r = 2.8m / 2 = 1.4m. The height is 4.2m. So, the volume of the tank is V = π * (1.4m)² * 4.2m.
Step 2: Calculate the cross-sectional area of the pipe. The formula for the area of a circle is A = πr², where r is the radius. The radius of the pipe is half its diameter, so r = 7cm / 2 = 3.5cm = 0.035m. So, the cross-sectional area of the pipe is A = π * (0.035m)².
Step 3: Calculate the volume of water flowing through the pipe per second. The volume of water flowing through the pipe per second is the cross-sectional area of the pipe times the flow rate. So, the volume of water flowing through the pipe per second is V = A * flow rate = π * (0.035m)² * 4m/sec.
Step 4: Calculate the time it takes to fill the tank. The time it takes to fill the tank is the volume of the tank divided by the volume of water flowing through the pipe per second. So, the time it takes to fill the tank is t = V_tank / V_pipe.
Now, you just need to plug in the values you calculated in steps 1, 2, and 3 into the formula in step 4 and solve for t. Don't forget to convert the time from seconds to minutes by dividing by 60.
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