This is a pond in the shape of a prism. It is completely full of water. Colin uses a pump to empty the pond. The level goes down by 20cm in the first 30 minutes. Work out how many minutes Colin has to wait for the pond to completely empty.

Volume of the prism is given by:
V=(base area)*(height)
thus:
base area=1/2(a+b)*h
=1/2(1.4+0.6)*2
=2 m²

Thus the volume will be:
V=2*1
V=2 m³

Volume after 30 min:
V=2×(0.8)
V=1.6 m³

Rate of emptying the tank is:
(2-1.6)/30=1/ 75 m³/min
time taken to empty the tank:
time=volume/rate
time=2/(1/75)
=150 min

Answer Link

ahirohit963 ahirohit963 · Answer 2 · 2021-10-29T15:01:16+02:00

To empty the tank completely, Colin has to wait 150 minutes for the water of the pond to at zero level.

Given :

A pond in the shape of a prism.

Colin uses a pump to empty the pond. The level goes down by 20 cm in the first 30 minutes.

Solution :

We know that the volume of the prism is given by,

[tex]\rm Volume = (Base\;Area)\times Height[/tex]

And also

[tex]\rm Base\; Area = \dfrac{1}{2}\times(1.4+0.6)\times 2[/tex]

[tex]\rm Base \;Area = 2\;m^2[/tex]

Now,

[tex]\rm Volume = 2\times1=2\;m^3[/tex]

Given that the level of pond goes down by 20 cm in the first 30 minutes. Therefore, the volume becomes,

[tex]\rm Volume = 2\times0.8=1.6\;m^3[/tex]

Now, the rate of emptying the tank is,

[tex]\rm =\dfrac{2-1.6}{30}=\dfrac{1}{75}\;m^3/min[/tex]

We also know that,

[tex]\rm time = \dfrac{volume }{rate}[/tex]

[tex]\rm time = \dfrac{2}{\dfrac{1}{75}}=150\;min[/tex]

Therefore, Colin has to wait 150 minutes for the pond to completely empty.

For more information, refer the link given below

https://brainly.com/question/13324776