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#1 2007-04-02 22:17:01

naheed
Member
Registered: 2007-04-02
Posts: 1

depth of pond - please help

Water flows through a pipe into an empty cylindrical tank.
The tank has a radius of 40 cm and a height of 110 cm.
(a) Calculate the volume of the tank.
(b) The pipe has a cross-sectional area of 1.6 cm^2.
The water comes out of the pipe at a speed of 14 cm/s.
How long does it take to fill the tank?
Give your answer in hours and minutes, correct to the nearest minute.
(c) All the water from the tank is added to a pond which has a surface area of 70 m^2.
Work out the increase in the depth of water in the pond.
Give your answer in millimetres, correct to the nearest millimetre.

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#2 2007-04-02 22:44:25

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: depth of pond - please help

(a) This is straightforward; I’ll leave you to do it yourself. smile

(b) First work out the volume of water that comes out of the pipe per second. In one second, 14 cm of water comes out; ∴ in one second, the volume of water that flows out is 14×1.6 cm[sup]3[/sup].

The time in seconds for the tank to fill is given by (volume of tank) ÷ (volume of water that flows out per second). So take the answer you get from (a) and divide it by 14×1.6. This will be in seconds, so you will need to convert to hours and minutes as specified.

(c) The tank’s volume of water is spread over an area of 70 m[sup]2[/sup]. Convert this to cm[sup]2[/sup]. Then use the formula (volume of tank) = (surface area of pond) × (increase in depth of the pond) to find the increase in depth of the pond, making sure you use consistent units. Finally, convert the answer you get for the depth increase to millimetres.

Last edited by JaneFairfax (2007-04-02 22:54:07)

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#3 2007-04-03 03:04:22

naheed
Member
Registered: 2007-04-02
Posts: 1

Re: depth of pond - please help

Thanks a lot for the answer and it's thorough explanation. Things are a lot clearer now.

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