Water flows from a tap. At the rate 27cm3 per second, into a rectangular container of length 60cm, breathe 30 cm and height 40 cm. If at 6.00 p.m. the container was half full, what will be the height of water at 6.04 pm?
v = l x w x h
= 60 x 30 x 40
=72,000cm^3
but at 6.00 p.m is half full
= 72,000/2 = 36,000cm^3
4mins = 240 secs
1s = 27cm^3
240secs = 240 x 27
= 6480cm^3
add to the half water in the container
= 36,000cm^3 + 6480cm^3
= 42,480cm^3
this means that, 42,480 cm^3 = 60 x 30 x h
solving for h, h= 23.60cm
and this is the required h
To determine the height of the water in the container at 6.04 pm, we need to calculate the amount of water that flows into the container between 6.00 pm and 6.04 pm and add it to the initial half-full height of the container.
First, let's calculate the amount of water that flows into the container in 4 minutes (from 6.00 pm to 6.04 pm). We know that the rate of water flow is 27 cm3 per second, so in 4 minutes (240 seconds), the volume of water flowing into the container is:
Volume = Rate × Time
Volume = 27 cm3/s × 240 s
Volume = 6480 cm3
Next, let's calculate the initial half-full height of the container. Since the container is rectangular with a length of 60 cm, breadth of 30 cm, and height of 40 cm, the volume when the container is half full is:
Half-Full Volume = Length × Breadth × Height / 2
Half-Full Volume = 60 cm × 30 cm × 40 cm / 2
Half-Full Volume = 36,000 cm3
Now, we can calculate the final height of the water in the container at 6.04 pm by adding the volume of water that flowed in (6480 cm3) to the initial half-full height of the container (36,000 cm3) and dividing it by the area of the base (length × breadth):
Final Height = (Half-Full Volume + Volume) / (Length × Breadth)
Final Height = (36,000 cm3 + 6480 cm3) / (60 cm × 30 cm)
Final Height = 42,480 cm3 / 1800 cm2
Final Height = 23.6 cm
Therefore, the height of the water in the container at 6.04 pm would be 23.6 cm.
22.7
4 minutes is 240 seconds.
So, the water will rise (27*240)/(60*30) cm
I expect you can use that to answer the question.