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Water flows through a circular pipe of cross-section area of 6.16cm² at a uniform speed of 10cm per second.At 6 a.m,water starts flowing through the pipe into an empty rectangular tank of base area 3m².

Class: Form 1

Subject: Mathematics

Topic: Rates, Ratios, Proportions and Percentages

Lesson Summary

Water flows through a circular pipe of cross-section area of 6.16cm² at a uniform speed of 10cm per second.At 6 a.m,water starts flowing through the pipe into an empty rectangular tank of base area 3m².
a)What is the depth of the water in the tank at 8.30a.m?
b)If the tank is 1.2metres high and has a hole at the bottom through which water leaks at the rate of 11.6cm³ per second,determine the time at which the tank will be filled.



Text Answer


a)What is the depth of the water in the tank at 8.30a.m?

Volume flowing into the tank per second =cross section Area x speed
=6.16cm² x 10cm/second =61.6cm³/second
q1942019251.png
1m³ x 61.6
1000000
0.0000616m3
From 6:00a.m to 8:30a.m =212hours (52x 3,600) =90,000seconds
q1b942019253.png
90,000 x 0.0000616 =0.5544m³
Volume of the water tank at 8:30a.m =0.5544M³
Volume of the rectangular tank = base area x depth
0.55443=3 x depth3

Depth = 0.5544 ÷3 = 0.1848M OR 18.48cm

b)If the tank is 1.2metres high and has a hole at the bottom through which water leaks at the rate of 11.6cm³ per second,determine the time at which the tank will be filled.

Volume of the tank =Base area x height
=3m² x 1.2m =3.6m³
In 1 second the water filled into the tank =0.0000616m³ and the water leaking out of the tank in 1 second is 0.0000116m³ so net volume flowing into the tank per second
=0.00006160-0.0000116 =0.00005M³
q1c942019300.png
𝟏 𝒙 𝟑.𝟔𝟎.𝟎𝟎𝟎𝟎𝟓==72,000 seconds
72,0003600= 20 hours
6:00 a.m + 20hours = 2600h – 2400h =2:00a.m the next day.

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